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  • Articles  (6,934)
  • Springer  (6,934)
  • 1990-1994  (6,770)
  • 1950-1954  (164)
  • Electrical Engineering, Measurement and Control Technology  (6,934)
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  • Articles  (6,934)
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  • 1
    Electronic Resource
    Electronic Resource
    Preface (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 153-154 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189871
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient derivation of the optimal mean-square binary morphological filter from the conditional expectation via a switching algorithm for discrete power-set lattice (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 409-430 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Once designed, implementation of an optimal mean-square binary morphological filter is extremely fast, especially when the erosions are implemented on a suitable parallel processor. On the other hand, optimal filter design involes a computationally burdensome search procedure that can, in practice, be intractable. The present paper provides an algorithm for filter design that is based on the relationship between the optimal morphological filter and the conditional expectation. The algorithm proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error by a minimal amount. It does so by switching observations between the 1-set and the 0-set of the conditional expectation. The switching algorithm is extremely efficient in many noise environments, and therefore provides a filter design that can be useful for online structuring-element updating. Owing to the relationship between stack and morphological filters, the algorithm is at once useful for finding optimal binary stack filters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223318
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  • 3
    Electronic Resource
    Electronic Resource
    Zero principles for implicit feedback systems (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 273-293 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A basic control engineer's adage-the poles of a feedback compensator become zeros of the closed-loop system-admits difficulties of interpretation even in the most simple of cases; that of single-input, single-output. An earlier investigation has provided an analysis of this adage in a module-theoretic context for systems in state space form while avoiding restrictive assumptions on system minimality or squareness. The main result is expressed concisely in terms of an exact sequence of modules which include Ω-zero modules corresponding to the feedback system and the plant. Extended zero modules of Ω-type incorporate both finite invariant zero structure, and generic zero information which occurs when a system fails to be right-invertible. In the case of compensation in the feedback path, this main exact sequence reduces to a mathematically clear expression of the aforementioned adage: the Ω-zero module of the feedback system is precisely the direct sum of the Ω-zero module of the plant and the system pole module of the feedback compensator. This paper extends the previous work in order to avoid assumptions on causality in the plant. Implicit dynamical systems are employed, in lieu of systems in state space form. Once again, it is not assumed that the system is one-to-one or onto; and so the concepts of generic zeros and their modules are brought into the arena of implicit systems. The implicit system itself is assumed in this work to be regular; however, decoupling zeros are permitted. Moreover, input-decoupling zeros and system pole feedback relationships are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188111
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  • 4
    Electronic Resource
    Electronic Resource
    Editorial (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 387-388 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183735
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  • 5
    Electronic Resource
    Electronic Resource
    A polynomial approach to deriving a state-space model of a periodic process described by difference equations (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 373-384 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract When the problem is considered of obtaining a periodic description in state-space form of a linear process which can be modelled by linear difference equations with periodic coefficients, it is natural to ask whether it is possible to preliminarily derive a polynomial equivalent form of such equations, which in the periodic case plays a role similar to the Rosenbrock's polynomial matrix description of a linear time-invariant process. In this paper a polynomial time-invariant description of a linear periodic process is introduced. It is shown that such a polynomial description gives a simple characterization of the dimension of the space of the solutions corresponding to the null input function, i.e., of the order of the periodic model under consideration. In addition, it allows us to introduce a transfer matrix for the computation of the output responses corresponding to null initial conditions, and to deduce conditions for the periodic model to be causal. These results, as well as the possibility of defining strict system equivalence between two periodic models through their time-invariant polynomial descriptions, in a similar sense as in the time-invariant case, show the relevance of such a polynomial time-invariant description for the problem under consideration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188117
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  • 6
    Electronic Resource
    Electronic Resource
    Feasibility study of parameter estimation of random sampling jitter using the bispectrum (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 435-453 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An actual sampling process can be modeled as a random process, which consists of the regular (uniform) deterministic sampling process plus an error in the sampling times which constitutes a zero-mean noise (the jitter). In this paper we discuss the problem of estimating the jitter process. By assuming that the jitter process is an i.i.d. one, with standard deviation that is small compared to the regular sampling time, we show that the variance of the jitter process can be estimated from thenth order spectrum of the sampled data,n=2, 3, i.e., the jitter variance can be extracted from the 2nd-order spectrum or the 3rd-order spectrum (the bispectrum) of the sampled data, provided the continuous signal spectrum is known. However when the signal skewness exceeds a certain level, the potential performance of the bispectrum-based estimation is better than that of the spectrum-based estimation. Moreover, the former can also provide jitter variance estimates when the continuous signal spectrum is unknown while the latter cannot. This suggests that the bispectrum of the sampled data is potentially better for estimating any parameter of the sampling jitter process, once the signal skewness is sufficiently large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183740
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  • 7
    Electronic Resource
    Electronic Resource
    Some results on sensitivity of general input-output systems (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 71-89 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider general input-output systems, which need not be of a feedback type, that are governed by nonlinear operator equations which relate the input, state, and output. Assuming that these equations depend on a parameterA which is allowed to vary in a neighborhood of a “nominal value”A 0 , we study the dependence of the output onA when the input is fixed. Essentially, we call a system insensitive if the output depends continuously onA. Two insensitivity concepts are introduced, and it is shown that certain monotonicity-like conditions ensure insensitivity. Also, several particular cases of the governing equations are studied. As examples, a control system described by a singular system of ordinary differential equations and a nonlinear feedback system are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183241
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  • 8
    Electronic Resource
    Electronic Resource
    On limit cycles inn-order direct-form digital filters (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 153-161 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The relationship between the elements in the vector of any limit cycle due to rounding in ann-order direct-form digital filter is established. Some bounds on the elements in such vectors are also determined. Sufficient conditions for the accessibility of period-r limit cycles due to rounding inn-order digital filters are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183768
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  • 9
    Electronic Resource
    Electronic Resource
    Direction-of-arrival estimation in applications with multipath and few snapshots (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 327-342 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper analyzes two direction-of-arrival (DOA) estimation algorithms used in the presence of multipath propagation and with very few snapshots. The conditional maximum likelihood (CML) algorithm and the method of direction estimation (MODE) are discussed. The estimates provided by these algorithms are shown to coincide for large number of snapshots or large signal-to-noise ratio. Necessary and sufficient conditions are derived for the algorithms to yield unique estimates. It is shown that their uniqueness conditions coincide with the minimal uniqueness condition on the array, that is independent of the algorithm used (if the array does not satisfy this minimal condition, no DOA estimation method can give unique estimates). Numerical examples are presented to demonstrate the theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187549
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  • 10
    Electronic Resource
    Electronic Resource
    Robust stability and senstivity of input-output systems over extended spaces (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 361-389 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In Part I of this paper we consider a general model of an input-output system governed by nonlinear operator equations that relate the system's input, state, and output, all of which are elements in extended spaces. This model encompasses feedback systems as a special case. Assuming that the equations governing the system depend on a parameterA that is allowed to vary in a neighborhoodN r (A 0) of a nominal valueA 0 in a linear space, we study conditions under which the system is stable for everyA ε Nr(A0), i.e., when the system exhibits robust stability. By stability we essentially mean that the input-output operator is continuous. Depending on the type of continuity of a map between two extended spaces, four concepts of robustness are introduced. The main results, Theorems 1 and 2, furnish sufficient conditions for a system to be robust in the respective sense. Basically, they show that if the nominal system satisfies a certain condition guaranteeing its stability, and the operators appearing in the governing equations depend continuously on the parameterA, then we have robust stability. As examples illustrating the applications of our results we discuss (1) a feedback-feedforward system, in particular the case when the extended space consists of locally square-integrable functions or functions continuous on [0, ∞), and (2) a time-varying dynamical system described by a linear vector differential equation, whose variables are continuous functions on [0, ∞) which decrease exponentially to zero ast → ∞. At the end of the paper some modifications of the presented theory are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187551
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  • 11
    Electronic Resource
    Electronic Resource
    Higher-order statistics-based input/output system identification and application to noise cancellation (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 485-511 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Higher-than-second-order statistics-based input/output identification algorithms are proposed for linear and nonlinear system identification. The higher-than-second-order cumulant-based linear identification algorithm is shown to be insensitive to contamination of the input data by a general class of noise including additive Gaussian noise of unknown covariance, unlike its second-order counterpart. The nonlinear identification is at least as optimal as any linear identification scheme. Recursive-least-squares-type algorithms are derived for linear/nonlinear adaptive identification. As applications, the problems of adaptive noise cancellation and time-delay estimation are discussed and simulated. Consistency of the adaptive estimator is shown. Simulations are performed and compared with the second-order design.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194885
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  • 12
    Electronic Resource
    Electronic Resource
    Analysis of weighted median filters based on inequalities relating the weights (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 115-136 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract By considering all orderings of the input samples, which are discrete-time continuous-valued, it is shown here that a weighted median (WM) filter of spanN can be specified unambiguously by 2N−1 consistent linear inequalities relating the weights. This specification is identical to that of a self-dual threshold function with the same weights. It is also shown that WM filters with symmetric weights can be specified by ternary threshold functions. Based on these inequalities, properties of WM filters which can be used to check equivalence of some WM filters are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189223
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  • 13
    Electronic Resource
    Electronic Resource
    Signal and image processing using three-dimensional binary ranking transforms (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 137-151 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Because binary mathematical morphology permits fast local neighborhood operations by flash conversion, it is used extensively in high-speed pattern-recognition computer systems. Further, since anyN-dimensional integer function may be represented by an (N + 1)-dimensional binary (bilevel) function, ordinary two-dimensional graylevel images become three-dimensional binary images. Thus these images may be processed by high-speed flash-conversion computers assuming that a sufficiently compact three-dimensional kernel can be devised. The tetradekahedron of the face-centered-cubic tessellation forms a perfect kernel in three-dimensions. Its neighborhood is compact. It has total symmetry with all 12 neighbors equidistant from the central element. Using this kernel a variety of useful three-dimensional morphological operations may be performed for target track detection, shaded graphics, data clustering, automated focusing, and spatial filtering.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189224
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  • 14
    Electronic Resource
    Electronic Resource
    On the performance of stack filters and vector detection in image restoration (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 153-169 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Two techniques for image restoration are compared in this paper. One is a technique based on the theory of optimal adaptive stack filtering; the other is a recently developed vector detection approach to image restoration. The primary difference between these two techniques is that the optimal detection technique exploits multilevela priori information, while the stack filter uses only single level zero crossing information. The design constraints for stack filters and vector detection are similar. Both approaches rely on the existence of a training sequence for the image source in order to obtain optimal processing. Adaptive stack filters do, however, require a training set of the noise while the optimal detection approach only needs a multivariate parametric representation. The image-restoration performance of these two methods is compared in a signal dependent noise environment characterizing imaging systems with speckle, film-grain, and Poisson shot noise. Comparisons are made using the mean absolute error measure as well as a subjective measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189225
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  • 15
    Electronic Resource
    Electronic Resource
    Losslessness and stability of LDI ladders and filters (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 325-352 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The stability of digital ladder filters close in form, via the lossless discrete integrator (LDI) transformation, to doubly terminatedLC Cauer ladder low-pass filters is studied. The LDI transformation does not necessarily map stable analogue into stable digital filters. Necessary and sufficient conditions for these digital filter to be lossless and for a corresponding doubly terminated filter to be stable are given. LDIs are often used in the design of switched capacitor (SC) filters. For this case we provide a threshold sampling rate above which the SC LDI filter retains the stability of the analogue filter. In spite of the stability problem with the LDI mapping, it has been observed that when applied to simulate analogue filters the resulting filter is stable. It can now be argued that, in these cases, other factors in the determination of the sampling rate leads typically to a choice that is also sufficiently above the threshold rate for stability. The theory described is also useful to derive more general digital filters and to perform the design of stable LDI filters exclusively in the Z-plane without reference to analogue prototypes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01293679
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  • 16
    Electronic Resource
    Electronic Resource
    On construction of coprime factorizations for nonlinear feedback control systems (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 285-307 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we describe a family of operators for constructing nontrivial left and right coprime factorizations under rather weak conditions for a large class of nonlinear feedback control systems that has a stabilizable or unstabilizable plant, using a common criterion of input-output stability. The proposed sufficiency and construction method are based on a generalization of the nonlinear Lipschitz operator theory formulated by us for such systems. This class of generalized nonlinear Lipschitz operators constitutes a very large family (an infinite-dimensional Banach space) of bounded nonlinear operators that describe (part of) the underlying systems. One of the main difficulties in constructing coprine factorizations for nonlinear feedback systems has been in taking care of the nonlinear composite and inverse operators that appear in the closed-loop configuration such that the overall feedback system is well defined in the sense of stability, causality, and uniqueness of the internal signals and such that the coprime factorizations can be achieved. In this paper we show how these difficult issues can be handled nicely under our framework of generalized nonlinear Lipschitz operator theory, at least for a very large class of nonlinear control systems. We give a simple illustrative example to show how these coprime factorizations can actually be characterized and constructed to yield explicit closed-form solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01293677
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  • 17
    Electronic Resource
    Electronic Resource
    Improved neural networks for analog-to-digital conversion (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 387-398 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we study the problem of designing a neural network that gives the correct binary representation of a given real number. Previously this problem has been studied by Tank and Hopfield. The network proposed by them exhibits “hysteresis” in the sense that the current vector of the network sometimes converges towards a binary vector that isnot the correct binary representation of the input current. The reason for this is that the network proposed by them has multiple asymptotically stable equilibria. In the present paper, we propose another neural network which has the property that it hasa single, globally attractive equilibrium for almost all values of the input current. Hence, irrespective of the initial conditions of the network, the current vector converges towards the correct binary representation of the input current.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190983
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  • 18
    Electronic Resource
    Electronic Resource
    On observability of singular systems (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 421-430 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Concepts of observability and strong observability for singular systems are introduced and characterized geometrically in terms of the system matrices without using the Weierstrass decomposition. Duality relations between observability and controllability and that between reachability and strong observability are established. A canonical form for the action of the output injection group on the set of observable systems is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190985
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  • 19
    Electronic Resource
    Electronic Resource
    Rotationally invariant pecstrum: A rotationally invariant object descriptor based on mathematical morphology (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 455-492 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Mathematical morphology is becoming increasingly important in industrial vision applications for object recognition and defect inspection. In this paper we define a new function based on mathematical morphology, which we named the Rotationally Invariant Pecstrum (RIP). The RIP is proven to be invariant under rotation regardless of the shape of the structuring element. This paper also discusses how to use the RIP as an object descriptor and studies the effect of using different structuring elements on recognizing objects of different shapes.
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    URL: http://dx.doi.org/10.1007/BF01219503
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  • 20
    Electronic Resource
    Electronic Resource
    Close-form coefficient expressions of typical two-dimensional band-select linear-phase FIR filters (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 493-508 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This work presents close-form formulas for typical two-dimensional bandselect linear-phase FIR filters (e.g., band-pass, high-pass, and band-stop filters) optimal in the least-squares sense. Cases of both circular and elliptical symmetry are considered. The formulas refer to the coefficients of the frequency sampling form of the frequency response. Therefore they can either be directly used for filter implementation, if the frequency sampling structure is adopted, or used to obtain the impulse response coefficients via an inverse FFT.
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    URL: http://dx.doi.org/10.1007/BF01219504
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  • 21
    Electronic Resource
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    Feedback neural networks: new characteristics and a generalization (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 263-278 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract New characteristics of feedback neural networks are studied. We discuss in detail the question of updating of neurons given incomplete information about the state of the neural network. We show how the mechanism of self-indexing for such updating provides better results than assigning ‘don't know’ values to the missing parts of the state vector. Issues related to the choice of the neural model for a feedback network are also considered. Properties of a new complex valued neuron model that generalizes McCulloch-Pitts neurons are examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189877
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  • 22
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    Chained eigenstructure assignment for strongly controllable singular systems (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 391-407 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper deals with chained eigenstructure assignment for strongly controllable singular systems of the form Êx (t)=Â x(t)+B u(t) with state feedback control of the formu(t)=Kx(t)+w(t). The development of our method depends crucially on the properties of standard form singular systems. The closed-loop system will satisfy the following requirements: regularity, impulse-free response and rankÊ arbitrary eigenvalues assignment. This parametric characterization conveniently organizes the nonunique gain matrixK to modify the dynamic response of the systems. The result can be used for discrete-time descriptor systems, in which a zero-value eigenvalue may well be a desired closed-loop eigenvalue. One illustrative example is included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223317
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  • 23
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    Statistical performance analysis of a fast stochastic gradient for constrained adaptive time delay estimation (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 453-464 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.
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    URL: http://dx.doi.org/10.1007/BF01223321
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  • 24
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    Fast algorithms for erasures and error correction in redundant residue number systems (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 503-531 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this work, we extend the coding theory approach to error control in redundant residue number systems (RRNS). The concept of erasure correction capability in RRNS is introduced. We derive the relationship between the minimum distance and the error detection and error/erasure correction capability. New computationally efficient algorithms are derived for simultaneously correcting single errors and multiple erasures and detecting multiple errors. These algorithms reduce the computational complexity of the previously known algorithms by at least an order of magnitude. Another attractive feature of the algorithms is that all the arithmetic operations are modulo operations. Consequently, the need to process large valued integers is avoided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188092
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  • 25
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    On real and complex normalizations (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 579-587 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a general expression relating the complex-normalized scattering matrix of ann-port network to that of its augmentedn-port network normalizing to then 1 −Ω resistances, where the Darlington equivalent network may be either reciprocal or nonreciprocal.
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    URL: http://dx.doi.org/10.1007/BF01188096
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  • 26
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    Regularity and singularity in linear-quadratic control subject to implicit continuous-time systems (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 19-30 
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    Notes: Abstract A linear-quadratic (LQ) control problem subject to a standard continuous-time system is called regular if the input weighting matrix is invertible, and singular if this is not the case. Consequently, optimal inputs for regular LQ problems are ordinary functions (state feedbacks), whereas optical controls for singular problems are in general distributions, e.g., impulses. We will show that regularity and singularity in LQ problems subject to ageneral (implicit) system depends not so much on the input weighting matrix, as on the property that the integrand of the cost criterion is a function only if inputs and state trajectories are, as is the case for LQ problems, subject to astandard system. In particular, we will provide a simple criterion for distinguishing between regularity and singularity in LQ problems subject to a general system. Our criterion is expressed in the system coefficients only and reduces to the classical one if the underlying system is standard.
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    Preface (1994)
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    Circuits, systems and signal processing 13 (1994), S. 119-119 
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    Explicit formulae for completions of linear time varying singular systems of differential equations (1994)
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    Circuits, systems and signal processing 13 (1994), S. 185-199 
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    Notes: Abstract Completions of linear time varying singular systems of the formE(t)x′(t)+F(t)x′(t)=f(t) are explicitly computed using recent results on rational matrix functions. The algorithm and the theory behind it are carefully described. Computational issues are discussed.
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    Spectral methods for the solution of linear descriptor systems using Fourier functions (1994)
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    Circuits, systems and signal processing 13 (1994), S. 225-239 
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    Notes: Abstract In this paper a spectral method using orthogonal periodic basis functions for the analysis of linear time invariant descriptor systems is discussed, and the case of the trigonometric Fourier functions is investigated in detail. The method is shown to be convergent, in the distributional sense. However, for any finite number of basis functions, the periodicity induced by the chosen basis can give rise to spurious impulsive components in the computed system response, even in the case of correct initial conditions.
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    Topological considerations for autoregressive systems with fixed Kronecker indices (1994)
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    Circuits, systems and signal processing 13 (1994), S. 295-308 
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    Notes: Abstract In this paper we will study topological properties of the class of proper and improperp×m transfer functions of a fixed McMillan degreen. A natural generalization of this class is all autoregressive systems of degreen under external system equivalence. The subset of irreducible systems has in a natural way the structure of a manifold and we show how to extend this topology to the set of all autoregressive systems of degree at mostn. We will describe the subset of systems with fixed Kronecker indicesv=(v1,...,v p ) as an orbit space, which will enable us to calculate the topological dimension for each collection of indicesv. Finally, we will describe the topological closure of those sets in the space of all autoregressive systems.
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    Output dynamics assignment for implicit descriptions (1994)
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    Circuits, systems and signal processing 13 (1994), S. 349-359 
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    Notes: Abstract It has been shown in [B.M.90] that non-square implicit differential equations allow for the description of variable structure systems (variable order, variable sign, variable parameters). We combine here the possible control strategy developed in [L.91] for rectangular systems (insuring a unique output behavior for the system compensated with a proportional or proportional and derivative state feedback) with the detector and the observer introduced in [B.M.90] in order to obtain a closed-loop system where the initial structure variation disappears on the output. We also give necessary and sufficient conditions for the free assignment of the associated output dynamics.
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    Higher order cumulants and cumulant spectra (1994)
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    Circuits, systems and signal processing 13 (1994), S. 391-402 
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    Notes: Abstract An exposition of joint cumulants and cumulant spectra is presented. A distinction is emphasized in this paper between the cumulant spectrum of a time series and its stationary version, here called apolyspectrum. The variance and covariance of the sample bispectrum is then derived using a relationship between cumulant spectra of the finite Fourier transform for the 2nd and 4th cumulant function, and the bispectrum and trispectrum of the time series.
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    On the detection of transient signals using spectral correlation (1994)
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    Circuits, systems and signal processing 13 (1994), S. 467-479 
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    Notes: Abstract The detection of a general class of transient (i.e., finite energy) signals in additive stationary interference using the spectral correlation function (second order cumulant spectrum) is presented. Observable features in the two-dimensional spectral correlation function due to properties of signals in the assumed class of transients are exploited to derive a detection statistic. The performance of the proposed detection statistic relative to a conventional power spectral detector is presented.
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    Development and application of a statistically based feature extraction algorithm for monitoring tool wear in Circuit Board Assembly (1994)
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    Circuits, systems and signal processing 13 (1994), S. 411-433 
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    Keywords: Statistics: Nonparametric time series estimation for pattern analysis ; Industries: Health monitoring and durability of rotating machinery ; Reliability: Incipient failure inspection/quality control/system safety
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    Notes: Abstract Vibroacoustic signals of rotating machinery are composed of sums of modulated periodicities, broadband random components, and occasionally a set of transient responses. These signals are not ergodic as the modulated periodicities are partially coherent. Progressive wear of the rotating machine causes the nonlinear structure of the received signal to intensify, and nonlinearity results in transfer of energy between harmonics of the signal's periodic components. Statistics developed from bispectrum and second-order cumulant spectrum estimates of the measured signal are combined with power spectrum amplitudes as feature inputs for standard multivariate classifiers. The higher-order statistics measure, respectively, the extent of nonlinearity and intermodulation of the received signal. Classification results of simulated and actual incipient wear data collected from a controlled experiment drilling circuit boards illustrate the potential of this novel statistical signal processing approach.
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    Geometric characterization of Lewis Structure Algorithm (1994)
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    Circuits, systems and signal processing 13 (1994), S. 255-272 
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    Notes: Abstract A geometric interpretation of the Lewis Structure Algorithm (LSA) is given in terms of precise projection maps directly defined from the (E, A, B, C) maps of the system. An extended version of LSA is offered which, in addition to this geometric information, also provides in a direct way, and within the same (E, A, B, C) class of models, a left inverse (if any) of the system. An example is given.
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    An intermediate algorithm for pole placement by output feedback in descriptor systems (1994)
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    Circuits, systems and signal processing 13 (1994), S. 329-345 
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    Notes: Abstract We consider the problem of control of linear, time-invariant, multivariable descriptor (implicit) systems. In particular we examine the effectiveness of an algorithm (which is a generalization of previous work in state space systems) for the design of an output feedback control giving pole placement in such systems. Conditions are presented which ensure that the algorithm produces the required control. We also address the important issue of uniqueness of solutions.
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    Preface (1994)
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    Circuits, systems and signal processing 13 (1994), S. 389-390 
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    Active sonar detection in multipath: A New bispectral analysis approach (1994)
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    Circuits, systems and signal processing 13 (1994), S. 455-466 
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    Notes: Abstract Detecting active sonar returns in multipath media is a central underwater signal processing problem. This paper studies a new approach to active sonar detection using bispectral analysis of sonar data. Its sensitivity to non-stationarities is used to develop a threshold detector that can be applied to broad classes of signals and noise. Precise statistical descriptions of the underwater medium and noise are not required. Theoretical analyses predicting its performance as a function of signal-to-noise ratio and time-bandwidth product are presented. Computer simulation experiments verify the results and show that its performance compares favorably to that of conventional detectors.
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    Signal detection using third-order moments (1994)
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    Circuits, systems and signal processing 13 (1994), S. 481-496 
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    Notes: Abstract The noise suppression capability of higher-order moments and spectra has made them attractive when the goal is to extract or reconstruct a signal that is contaminated by multivariate Gaussian noise or certain types of non-Gaussian noise. Two new detectors, one centralized and one distributed, which are based on the third-order moment of the data are proposed. The asymptotic performance of the centralized detector and the asymptotic distribution of the components of the distributed detector are analyzed. Further, the performance of these detectors is simulated and compared to that of the matched filter for three different types of interference: Gaussian noise, Gaussian noise corrupted by a sinusoid with random phase, and Arctic under-ice noise.
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    Robustness of representations in multilayer feedforward neural networks (1993)
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    Circuits, systems and signal processing 12 (1993), S. 211-221 
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    Notes: Abstract Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper • Rigorously establishes the robustness of feedforward network realizations. • Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations toL 1 andL 2 functions by networks, for quite general activation functions. The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases ofL 1 andL 2 functions.
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    Control of linear systems under state-control constraints (1994)
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    Circuits, systems and signal processing 13 (1994), S. 361-372 
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    Notes: Abstract We investigate the controller design problem for linear systems in which the state and the controls are subject to static linear constraints. We give necessary and sufficient conditions for the existence, and present a complete parametrization of all stabilizing controllers. This parametrization allows us to transform the constrained control problem into a standard problem which can be solved using usualH 2 orH ∞ optimization methods. The approach is illustrated by a simple numerical example showing the various steps of the proposed algorithm.
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    Limitations on the use of discrete linear models of continuous random processes (1994)
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    Circuits, systems and signal processing 13 (1994), S. 403-410 
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    Notes: Abstract A continuous stationary signal possessing non-Gaussian higher order statistics cannot be correctly modelled by any discrete process based on passing independently and identically distributed noise through a linear filter. In particular, it is shown that at third order there exists no discrete skewed linear model with a discrete bispectrum that is the same as that obtained from the Nyquist samples of any continuous stationary process. The nature of the problem is elucidated and an alternative method for modelling the third order statistics of continuous stationary processes is proposed.
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    Comments on “Fault prediction for analog circuits” (1990)
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    Circuits, systems and signal processing 9 (1990), S. 501-502 
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    Reply to comments on “Fault prediction for analog circuits” (1990)
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    Circuits, systems and signal processing 9 (1990), S. 503-503 
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    Further comments on “Fault prediction for analog circuits” (1990)
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    Circuits, systems and signal processing 9 (1990), S. 505-505 
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    Symmetric matrices associated with a nonnegative matrix (1990)
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    Circuits, systems and signal processing 9 (1990), S. 171-180 
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    Notes: Abstract For ann-by-n nonnegative matrixP, we consider the entrywise harmonic meanH, geometric meanG, and arithmetic meanA, ofP and PT. Simple proofs are given for the inequalities ρ(H)≤ρ(G)≤ p(P)≤ ρ(A), and attention is focused upon characterization of the case of equality in each of these six inequalities. In caseP is irreducible, ρ(G)=p(P) exactly whenP is diagonally similar to a symmetric matrix, and several other equivalent conditions for diagonal symmetrizability ofP are collected together here. Other conditions which arise involve further variations upon symmetry, and may be viewed as algebraic descriptions of various features of symmetry. A tool of interest is a slight variation upon a recent characterization of the Perron root.
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    Shorted matrices in star and related orderings (1990)
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    Circuits, systems and signal processing 9 (1990), S. 197-212 
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    Notes: Abstract A new class of shorted operators is considered. The shorted operator has an intimate relationship with electrical networks and has been extensively studied. In this work we consider the class of matrices with row and column spans in specified linear subspaces and dominated in a given partial order by a matrixA. If this class of matrices has an unique maximal element under the partial order, then this maximal element is called the shorted matrix ofA relative to the given linear subspaces and the relevant partial order. We study the shorted matrix under the star order of Drazin, the minus order, and also under partial orders induced by the minimum norm and least squares g-inverses. The parallel sum of matrices is intimately related to the shorted matrix and results are given for parallel addition.
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    An alternate variational characterization of matrix Riccati equation solutions (1990)
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    Circuits, systems and signal processing 9 (1990), S. 223-228 
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    Notes: Abstract A new variational characterization of the solution of a matrix Riccati equation is presented. The characterization is given as the maximum Hermitian matrix that makes a certain compound matrix Hermitian positive semidefinite. The shorted operator (Schur complement) applied to the compound matrix produces the Riccati equation.
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    Eigenstructure methods for direction finding with sensor gain and phase uncertainties (1990)
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    Circuits, systems and signal processing 9 (1990), S. 271-300 
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    Notes: Abstract An eigenstructure-based method for direction finding in the presence of sensor gain and phase uncertainties is presented. The method provides estimates of the Directions of Arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor in the observing array. The technique is not limited to a specific array configuration and can be implemented in a'ny eigenstructure-based DOA system to improve its performance.
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    Analysis of systems subject to parameter uncertainties: Application of interval analysis (1990)
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    Circuits, systems and signal processing 9 (1990), S. 319-341 
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    Notes: Abstract The effects of system parameter uncertainties on system performance are always of great concern to the system designer. It is desirable to knowa priori estimates of the system response, subject to parameter uncertainties. In the following we propose using interval analysis techniques to establish estimates of system performance (e.g., envelopes of time response and frequency response). The results which we obtain constitute generalizations of existing work. Specifically, existing results address systems which are described by linear ordinary differential equations which are endowed with a single parameter belonging to an interval. In the present results we address systems described by linear or nonlinear ordinary difference equations endowed with more than one parameter belonging to intervals.
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    Some results on robust stability of general input-output systems (1990)
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    Circuits, systems and signal processing 9 (1990), S. 343-364 
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    Notes: Abstract We consider general input-output systems governed by nonlinear operator equations that relate the system's input, state, and output. The systems under consideration need not be of a feedback type. Assuming that the governing equations depend on a parameterA in a linear space that is allowed to vary in a vicinity Nr(A0) of a “nominal” valueA 0, we study conditions under which the system is stable for each A∈Nr (A0), i.e., when the system is robust. By stability we essentially mean that the input-output map is continuous. Depending on the type of continuity used, two concepts of robustness are introduced. The main theorem shows that a certain generalized monotonicity condition imposed on the nominal system combined with a Lipschitz-like condition imposed on the perturbed system guarantees robustness. Moreover, several particular cases of the governing equations are investigated. As examples, we consider (1) a singular system of nonlinear ordinary differential equations (a semistate equation), (2) a feedback system, and (3) a feedback, feedforward system. At the end of this paper some extensions and modifications of the presented theory are discussed.
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    On a geometrical interpretation of differential-algebraic equations (1990)
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    Circuits, systems and signal processing 9 (1990), S. 367-382 
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    Notes: Abstract The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE, and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lower-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena.
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    Stability regions for second-order fixed-point digital filters in coupled form (1990)
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    Circuits, systems and signal processing 9 (1990), S. 409-420 
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    Notes: Abstract The influence of the asymmetry parameterk on the extent and form of the stability region for second-order fixed-point coupled-form digital filters is analyzed. In particular, by extending the results of a previous paper by the same authors, the stability regions for filters with roundoff quantizers are first shown. Then, the corresponding results for filters with either two or four value-truncation quantizers are derived. It turns out that the shape of the stability areas is rather odd because of the asymmetry of the quantization characteristic.
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    Discrete-timep-powers and stability (1990)
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    Circuits, systems and signal processing 9 (1990), S. 435-448 
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    Notes: Abstract Iterated-integral operators calledp-powers arise in the theory of representations of nonlinear systems. In a recent paper, necessary and sufficient conditions are given for such operators to be stable in a standard sense, and it is shown that a well-known sufficient condition is not necessary for allp ≥ 2. Here corresponding results are given for discrete-time cases.
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    Application of signal subspace approach to high-resolution narrowband array processing (1990)
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    Circuits, systems and signal processing 9 (1990), S. 421-433 
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    Notes: Abstract The paper first briefly reviews some subspace techniques for high-resolution array processing. It is shown that existing high-resolution techniques like the MUSIC algorithm are based on visual inspection of the spatial spectrum. It is not a scientifically valid means of assessing resolution of a spectrum estimator. The paper then proposes a technique based on a combination of optimal processing and signal subspace extraction for high-resolution array processing. Numerical results show that the proposed technique not only achieves superresolution of the spectrum, but also provides power estimates of the arrivals.
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    A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures (1990)
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    Circuits, systems and signal processing 9 (1990), S. 449-500 
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    Notes: Abstract Fourier transform algorithms are described using tensor (Kronecker) products and an associated class of permutations. Algebraic properties of tensor products and the related permutations are used to derive variants of the Cooley-Tukey fast Fourier transform algorithm. These algorithms can be implemented by translating tensor products and permutations to programming constructs. An implementation can be matched to a specific computer architecture by selecting the appropriate variant. This methodology is carried out for the Cray X-MP and the AT&T DSP32.
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    A necessary and sufficient condition for right coprime factorization of nonlinear feedback systems (1993)
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    Circuits, systems and signal processing 12 (1993), S. 489-492 
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    Notes: Abstract In this short note, we establish a simple, yet precise, necessary and sufficient condition for the “right coprime factorization” of a nonlinear feedback control system. As a consequence, we also obtain similar conditions for the “stable right coprime factorizations ” of the nonlinear feedback control system.
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    Analysis of a PRSA generator (1993)
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    Circuits, systems and signal processing 12 (1993), S. 557-566 
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    Notes: Abstract The pseudorandom sequence of arrays (PRSA) and a method to generate it was reported earlier by the authors. This paper presents another method to generate a PRSA. The mathematical recursion describing the PRSA and some of its properties are discussed.
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    Well-posed nonlinear problems in integrated circuits modeling (1991)
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    Circuits, systems and signal processing 10 (1991), S. 53-69 
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    Notes: Abstract In this paper we study the problem (E) + (BC) + (IC) (see below) which represents a model for integrated circuits. We assume that the distributed parametersr(x) andc(x) are nonconstant, dielectric leakages depend on thex-coordinate as well as the voltage level, while the interconnecting multiport is nonlinear and possibly multivalued.
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    Zero structures at infinity of linear periodic systems (1991)
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    Circuits, systems and signal processing 10 (1991), S. 91-100 
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    Notes: Abstract The zero structure at infinity of a linear periodic system can be studied following two different approaches. One is based on the Periodic Invariant Subspace Algorithm and it gives rise to the notion of periodic structure at infinity. The second is based on the representation of a periodic system by means of a family of stationary systems and it allows the definition of a notion of zero structure. In this paper these two approaches are described and analysed in order to compare the structural information contained in the sets of invariants that they define. As a result we have that the zero structure can be derived by the periodic structure.
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    Large-scale dynamical interconnections of stochastic singular systems (1991)
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    Circuits, systems and signal processing 10 (1991), S. 115-133 
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    Notes: Abstract Large-scale dynamical interconnections of systems may not be well defined in the sense of having unique solutions for all inputs. We provide tests that show when the overall system is well defined. In a stochastic interconnected system, there is the additional problem that the composite system may be “stochastically ill defined” in the sense that derivatives of white noise may appear. We provide a test that shows when the interconnected systems is stochastically well defined. It is also demonstrated how to obtain a state-variable representation of the interconnected system, when one exists, on a subspace of the original descriptor-variable space. All of our results are based on “structure algorithms” for singular systems which use stable numerical operations on the original system and interconnection matrices.
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    Generalized Morse theory and its applications to control and stability analysis (1991)
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    Circuits, systems and signal processing 10 (1991), S. 175-209 
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    Notes: Abstract This paper extends Morse theory to noncompact manifolds which is important since in many engineering applications the manifolds involved are usually noncompact. To demonstrate the application, generalized Morse theory is used to estimate the number of unstable equilibria on the stability boundary. The engineering significance of the estimation is explained in the paper.
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    Convergence analysis of an adaptive pseudolinear-regression notch filtering algorithm (1991)
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    Circuits, systems and signal processing 10 (1991), S. 245-259 
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    Notes: Abstract This paper analyzes the convergence properties of an adaptive pseudolinear regression notch filtering algorithm recently proposed in the literature for estimating the frequencies of multiple sine waves from measurements corrupted by possibly colored additive noise. Simple necessary and sufficient conditions for the local convergence of this algorithm to the true frequency values are derived. It is shown that the algorithm has an interesting decoupling property in the sense that satisfaction of the convergence condition by a certain frequency implies local convergence to that frequency no matter whether the other frequencies satisfy or do not satisfy the convergence conditions. However, it is also shown that the algorithm is not generally convergent and, therefore, cannot be recommended for widespread use in applications. Numerical examples are used to illustrate the main points in the theoretical analysis.
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    Comparative performance study of element-space and beam-space MUSIC estimators (1991)
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    Circuits, systems and signal processing 10 (1991), S. 285-292 
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    Notes: Abstract The goal of this paper is to show that in large samples the variances of the direction-of-arrival (DOA) estimates provided by the element-space MUSIC (i.e., MUSIC applied directly to the sensor output data) are always less than the corresponding variances associated with the beam-space MUSIC (i.e., MUSIC applied to spatially filtered sensor data).
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    The classification properties of the pecstrum and its use for pattern identification (1991)
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    Circuits, systems and signal processing 10 (1991), S. 293-326 
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    Notes: Abstract In this paper the shape information contents of a morphological vector descriptor, called “pecstrum” (pattern spectrum), are investigated. The pecstrum is then used for aircraft recognition and classification. The pecstrum is a simple vector descriptor which provides information on the way the area of the object is distributed from the fine details to its bulky contents. Although some of its properties have already been reported [3], [4], [14], [23], the use of the pecstrum as a classification tool has not been given appropriate emphasis. At the beginning of the paper some introductory material on mathematical morphology and the pecstrum is presented for the reader who is not familiar with the relevant terminology. Next the shape information which the pecstrum conveys is analyzed and its classification properties are considered. New concepts such as the “pecstral” space and the cumulative pecstral transformation are introduced and explained. The performance of the pecstrum in certain recognition problems is also examined. The concept of “B-shapiness” is redefined and the relation between the pecstrum and the ratio area/perimeter2 is established. The “pseudopecstrum” is then introduced and its information contents and classification properties are compared with those of the conventional pecstrum. The use of pecstrum in estimating object orientation is also addressed. Finally, the recognition and classification capabilities of the pecstrum are tested using a large number of binary objects (airplanes). The performance limit of the pecstrum for efficient object classification, as the size of the objects decreases, is examined and the factors which affect this limit are discussed. The classification results are compared with those obtained using invariant moments.
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    Editorial (1992)
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    Circuits, systems and signal processing 11 (1992), S. 3-4 
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    Duality, observability, and controllability for linear time-varying descriptor systems (1991)
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    Circuits, systems and signal processing 10 (1991), S. 455-470 
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    Keywords: 34A08 ; 93B07 ; 93B15 ; 93C15 ; 93C50 ; Key words ; Descriptor ; Singular ; Differential-algebraic ; Observability ; Controllability ; Duality ; Structural forms
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    Notes: Abstract A characterization of observability for linear time-varying descriptor systemsE(t)x′(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x′(t)+F(t)x(t)=f(tt).
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    Preface (1992)
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    Circuits, systems and signal processing 11 (1992), S. 5-6 
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    Use of trellis diagrams in state estimation in blocks for nonlinear discrete dynamic systems with aKth-order memory (1991)
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    Circuits, systems and signal processing 10 (1991), S. 3-14 
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    Notes: Abstract A new suboptimum estimation scheme is proposed for nonlinear discrete dynamic systems with aKth-order memory. These systems are first represented by trellis diagrams, and then states are estimated by the Viterbi algorithm of information theory. The state and observation models of the proposed scheme can be nonlinear functions of the disturbance noise, observation noise, and present and past discrete values of the state, whereas the models of the classical estimation algorithms, such as the extended Kaiman filter, must be linear functions of the disturbance noise and observation noise. States are estimated in blocks, which results in an estimation scheme whose implementation requries a constant memory.
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    Parameter estimation and spectral analysis of the discrete nonlinear secondorder Wiener filter (NSWF) (1991)
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    Circuits, systems and signal processing 10 (1991), S. 31-51 
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    Notes: Abstract In many problems of digital signal processing, it is required to determine a model matching the statistics of a given observation of a generally non-Gaussian random process. Because of the wide range of systems that can be represented by Volterra series and Wiener expansions, the discrete nonlinear second-order Wiener filter (NSWF) driven by white Gaussian noise has been used in this study to match the statistics of a discrete zero-mean stationary non-Gaussian random process. First, we derive the autocorrelation function and show that it does not provide sufficient information necessary for estimating the parameters of the proposed model. Next, we derive the third-order moment sequence and show that it provides additional information that can be used in conjunction with the autocorrelation function to solve the problem. The power spectrum and bispectrum of the discrete NSWF have been also derived.
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    An elementary proof of the Routh-Hurwitz stability criterion (1991)
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    Circuits, systems and signal processing 10 (1991), S. 101-114 
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    Notes: Abstract This paper presents an elementary proof of the well-known Routh-Hurwitz stability criterion. The novelty of the proof is that it requires only elementary geometric considerations in the complex plane. This feature makes it useful for use in undergraduate control system courses.
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    On-line estimation of signal and noise parameters with application to adaptive Kalman filtering (1991)
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    Circuits, systems and signal processing 10 (1991), S. 137-152 
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    Notes: Abstract This paper presents two algorithms for on-line estimation of the optimal gain of the Kalman filter applied to sensor signals when the signal-to-noise ratio is unknown. First-order spectra of a pure signal and colored measurement noise have been assumed. The proposed adaptive Kalman filtering algorithms have been tested for various spectra of the pure signal and noise, and for various signal-to-noise ratios. The effect of the length of an adaptation step and a sampling frequency on the mean square errors of the pure signal estimation has also been examined. Although the test have been performed for stationary signals, the algorithms presented can also be used successfully for time-varying sensor signals when the signal-to-noise ratios vary very slowly in comparison with the length of the adaptation step. The results are helpful for designers who synthesize optimal linear digital filters for sensor signals with first-order spectra and colored measurement noise. The estimation error curves presented enable designers to determine the noise reduction attainable for particular applications of the adaptive Kalman filtering algorithms.
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    A Kalman filtering technique for certain Markov chains (1991)
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    Circuits, systems and signal processing 10 (1991), S. 211-219 
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    Notes: Abstract In this paper an efficient decoupling Kalman filtering technique is applied to certain Markov chains with finite-dimensional stationary state-transition matrices. For optimal estimates of a Markov chain with ann-dimensional stationary statetransition matrix, the resultant computational algorithm consists ofn-1 simple one-dimensional recursive formulas.
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    On reduced polynomial-based split algorithms (1991)
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    Circuits, systems and signal processing 10 (1991), S. 263-284 
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    Notes: Abstract In this work we analyze the mathematical structure associated with the split algorithms for computing the reflection coefficients for a given real, symmetric, positive-definite Toeplitz matrix. A new form of three-term recurrence relation is derived and computationally efficient alternatives to the Levinson-Durbin, Schur, lattice, and normalized lattice algorithms are obtained. The computational complexity of the new algorithms is the same as those of the split algorithms described in the recent literature. The relationships between the various algorithms are also established. These algorithms also provide further insight into the mathematical properties of the structurally rich Toeplitz matrices.
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    A fast perturbation method for the design of linear phase fir digital filters of finite wordlength using single-frequency filters (1991)
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    Circuits, systems and signal processing 10 (1991), S. 233-244 
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    Notes: Abstract In this paper a fast perturbation algorithm for the design of linear phase FIR digital filters of finite wordlength is presented. The original set of filter coefficients are obtained using the Parks-McClellan algorithm, then a small perturbation is given to these sets of coefficients. The peak deviations corresponding to the rounded set of coefficients obtained from the original and the perturbed sets are compared and the set of coefficients with the lower value of peak deviation is stored as the best set of coefficients. A further perturbation is given to the infinite precision coefficents and these are rounded to the required wordlength. Comparison is made between these rounded sets and the present best set with respect to peak deviation and the better set is stored as the best set of coefficients. This process is repeated for a finite number of times or until the peak deviation is sufficiently low. To obtain the compensating filter coefficients single-frequency filters are used. Mathematical justification for the single-frequency design is given. Important results for a large number of design examples are presented to illustrate the speed and effectiveness of the algorithm.
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    On an existence and uniqueness theory for nonlinear differential-algebraic equations (1991)
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    Circuits, systems and signal processing 10 (1991), S. 343-359 
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    Notes: Abstract An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our notions are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example.
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    Design of universal, variable frequency range FIR digital differentiators (1992)
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    Circuits, systems and signal processing 11 (1992), S. 431-439 
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    Notes: Abstract An efficient design of digital differentiators (DD), with a variable frequency range of operation at low and midband frequencies, has been proposed. Implemented as a Taylor structure, a DD designed for orderN can be made to function as a universal configuration giving optimal transfer functions for all possible ordersN, without changing the coefficients.
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    An improvement on the digital redesign method based on the block-pulse function approximation (1993)
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    Circuits, systems and signal processing 12 (1993), S. 37-49 
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    Notes: Abstract This paper proposes an effective method to improve the digital redesign method via the block-pulse function approach. The coefficients of the block-pulse function expansion are exactly evaluated such that the desired digitally redesigned feedback gain and forward gain will be obtained. A numerical example is given to demonstrate the effectiveness of the proposed method.
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    Interval-analysis techniques in linear systems: An application in power systems (1993)
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    Circuits, systems and signal processing 12 (1993), S. 51-60 
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    Notes: Abstract In this paper we apply the technique of interval analysis to get bounds on the initial value response of a linearized single machine infinite bus problem when a parameter is varied. It is generally believed that responses for parameter variations in an interval should lie within the responses for the extremums of the parameter variations. This is not generally true and our example demonstrates this. The interval-analysis technique permits getting the overall bound on the response. Further experimentation also revealed that the method has some limitations particularly involving lightly damped long-term dynamics. The technique is useful in finding the robustness of a particular design such as the power system stabilizer for parameter variations.
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    Comparative performance study of SVD-based and QRD-based high-order Yule-Walker methods for frequency estimation (1993)
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    Circuits, systems and signal processing 12 (1993), S. 105-117 
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    Notes: Abstract The high-order Yule-Walker (HOYW) method of sinusoidal frequency estimation based on a singular value decomposition (SVD) is known to have excellent statistical performance. Here, we show that the SVD-based step of the HOYW method can be replaced by a computationally more convenient QR decomposition (QRD)-based step, without affecting the asymptotic properties of the frequency estimates.
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    Estimation and setting starting values in ARMA algorithms (1993)
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    Circuits, systems and signal processing 12 (1993), S. 85-103 
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    Notes: Abstract For the given observations set of the ARMA (autoregressive moving average) process, the likelihood function depends, not only on model parameters, but on the starting values of the input and output. Therefore, it is called theconditional likelihood function. Theunconditional likelihood function can be obtained in two ways. The first is to set the starting values to zero, as is often done, and the second is to set them to the properly estimated values. The difference between these two types of likelihood functions is significant when the given data sequence is short, and any of the zeros of the moving average part is close to the boundary of the unit circle. In this paper the direct method of starting value estimation and its application to two off-line ARMA estimation algorithms, the maximum likelihood (ML) algorithm and the iterative inverse filtering (ITIF) algorithm, is proposed. Experimental results prove both increased efficiency and stability of these algorithms. The importance of setting the starting values properly is also significant when the recursive algorithm, with previously estimated parameters, has to be restarted. The advantage of the proposed reinitialization method is shown on the recursive lattice algorithm working in the block mode.
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    Editorial (1993)
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    Circuits, systems and signal processing 12 (1993), S. 151-151 
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    Classification of infinite networks and its application (1993)
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    Circuits, systems and signal processing 12 (1993), S. 133-149 
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    Notes: Abstract In this paper we consider nonlinear, infinite networks of purely resistive type where the voltage across a branch of the network is proportional to a fixed power of the current flowing in the branch. It is known that the study of currents in such networks amounts to studying the space of the functions on a network which have finite Dirichlet sums of orderp. Such a study was carried out in [7], [9], and [11]–[14] under the assumption that every node is connected to only finitely many different nodes of the network. In this paper we drop this assumption and work with general countable networks. We prove that most results of the locally finite case, and especially the classification theory, hold true in a more general context. Moreover, we give necessary and sufficient conditions for a network to have only constant Dirichlet finitep-harmonic functions. The relationship with discrete Markov processes is also pointed out.
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    Rapid backpropagation learning algorithms (1993)
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    Circuits, systems and signal processing 12 (1993), S. 155-175 
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    Notes: Abstract One of the major drawbacks of the backpropagation algorithm is its slow rate of convergence. Researchers have tried several different approaches to speed up the convergence of backpropagation learning. In this paper, we present those rapid learning methods as three categories, and implement the representative methods of each category: (1) for the numerical method based approach, the Aitken's Δ2 process, (2) for the heuristics based approach, the dynamic adaptation of learning rate, and (3) for the learning strategy based approach, the selective presentation of learning samples. Based on these implementations, the performance is evaluated with experiments and the merits and demerits are briefly discussed.
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    Morphology neural networks: An introduction with applications (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 177-210 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The area of artificial neural networks has recently seen an explosion of theoretical and practical results. In this paper, we present an artificial neural network that is algebraically distinct from the classical artificial neural networks, and several applications which are different from the typical ones. In fact, this new class of networks, calledmorphology neural networks, is a special case of a general theory of artificial neural nets, which includes the classical neural nets. The main difference between a classical neural net and a morphology neural net lies in the way each node algebraically combines the numerical information. Each node in a classical neural net combines information by multiplying output values and corresponding weights and summing, while in a morphology neural net, the combining operation consists of adding values and corresponding weights, and taking the maximum value. We lay a theoretical foundation for morphology neural nets, describe their roots, and give several applications in image processing. In addition, theoretical results on the convergence issues for two networks are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189873
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    Recent progress on higher order moment neural arrays (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 309-329 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Higher order moment computations are generally necessary wherever the recognition task exceeds the confines of linearity. This paper provides an overview of recent progress on a specific neural network design, which explicitly uses higher order moment information. Attention is focused on the training algorithms used in the design and on network performance in prototype applications.
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    URL: http://dx.doi.org/10.1007/BF01189879
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    On the existence and uniqueness of solutions for implicit linear systems on finite interval (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 375-390 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In the present paper we study the problem of the existence and uniqueness of solutions of implicit systems considered on a finite interval of time. We consider two kinds of existence problems: input-acceptance and input-acceptance when the boundary conditions of a corresponding trajectory are set to zero, and two kinds of uniqueness problems: output uniqueness and output uniqueness when the boundary conditions of the corresponding trajectory are unknown. Geometric conditions for all of these notions are given, and the duality of these notions is studied.
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    URL: http://dx.doi.org/10.1007/BF01223316
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    Statistical analysis of decentralized MUSIC (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 443-454 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For large-array processing problems there is a need for decentralized methods that are computationally efficient. A decentralized variant of the MUSIC algorithm, proposed in the literature, is here analysed from a statistical viewpoint, assuming that a large number of snapshots is available. As intuitively expected, the centralized MUSIC algorithm is more accurate than both the local and decentralized versions of MUSIC. More surprisingly, the decentralized variant of MUSIC is not always more accurate than the local MUSIC estimates. The theoretical analysis is supported by numerical examples.
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    URL: http://dx.doi.org/10.1007/BF01219502
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    Performance of direction-finding systems with sensor gain and phase uncertainties (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 3-35 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we study the performance of direction-finding systems which attempt to estimate unknown array parameters (such as sensor gains and phases) in addition to the estimation of the directions of arrival (DOA), as a way of performing array self-calibration. We develop compact closed form expressions for the Cramér-Rao bound associated with the joint estimation of DOAs, gains, phases, and the signal covariance matrix. By evaluating the Cramér-Rao bound for selected cases we gain some insight into the performance of direction-finding systems in the presence of gain and phase uncertainties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183145
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    Some results on sensitivity and robust stability of input-output systems governed by integral and differential equations (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 61-83 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider input-output systems (not necessarily of feedback type) on the time domain [0, ∞) which are governed by nonlinear vector integral or differential equations that relate the input and the output. Assuming that these equations depend on a parameterA, describing perturbations, which is allowed to vary in a vicinity of a nominal valueA 0 in a linear space, we study how strongly the output is affected by changes of (a)A 0 when the input is fixed (insensitivity), and (b) the input whenA is fixed withA A 0 being not too large (robust stability). The results are based on the theory of input-output systems over abstract extended spaces given in Parts I and II of [3]. We discuss nominal systems described by nonlinear Volterra and differential equations, and consider two types of possible perturbations. We also prove a simple result on systems governed by singular differential equations whose perturbations can change the order of the system.
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    URL: http://dx.doi.org/10.1007/BF01183148
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    A new family of biquads with applications to MOSFET-C filters (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 119-131 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new family of RC-active biquadratic building blocks are proposed in this communication. These biquads are especially designed for MOSFET-C applications, since they achieve a complete MOS nonlinearity cancellation. The proposed circuits can realize all the generic transfer functions such as lowpass, highpass, bandpass, band-rejection, and allpass. They also enjoy low passband sensitivities with respect to passive elements. The gain-bandwidth product-sensitivity is investigated too. An example of a high Q-bandpass filter is given with its Monte-Carlo simulation to verify its sensitivity performance.
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    URL: http://dx.doi.org/10.1007/BF01183151
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    A neural network approach to the traffic control problem in reverse baseline networks (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 247-261 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A neural network for the traffic control problem applied to reverse baseline networks has been proposed in this paper. This problem has been first represented by an energy function. A neural network is applied for maximizing the energy of the function under the constraints of the reverse baseline network. The number of iteration steps in our neural network is limited by a performed upper bound O(n), wheren is the size of ann ×n network. The throughputs of our neural network have been shown by the empirical results to be better than the conventional algorithm (modified Bipartite Matching Algorithm) when the packet densities rise higher than 50%.
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    URL: http://dx.doi.org/10.1007/BF01189876
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    Neural network constructive algorithms: Trading generalization for learning efficiency? (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 331-374 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract There are currently several types of constructive, (or growth), algorithms available for training a feed-forward neural network. This paper describes and explains the main ones, using a fundamental approach to the multi-layer perceptron problem-solving mechanisms. The claimed convergence properties of the algorithms are verified using just two mapping theorems, which consequently enables all the algorithms to be unified under a basic mechanism. The algorithms are compared and contrasted and the deficiencies of some highlighted. The fundamental reasons for the actual success of these algorithms are extracted, and used to suggest where they might most fruitfully be applied. A suspicion that they are not a panacea for all current neural network difficulties, and that one must somewhere along the line pay for the learning efficiency they promise, is developed into an argument that their generalization abilities will lie on average below that of back-propagation.
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    URL: http://dx.doi.org/10.1007/BF01189880
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    A general study of maximal robust stability regions (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 15-30 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In the study of robust stability, the largest coefficient region of a given stable polynomial that guarantees stability preservation under perturbation of coefficients is to be determined. A general consideration including both Hurwitz and Schur polynomials is treated in this paper. For this purpose, the notion ofperturbation constant is introduced. As a consequence of our results, we also introduce a general Kharitonov-type stability test which is based on testing the stability and perturbation constant of a single polynomial.
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    URL: http://dx.doi.org/10.1007/BF01183238
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    CAS-CAS transform for 2-D signals: A few applications (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 163-173 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A few applications of a separable Hartley-like (CAS-CAS) transform in two-dimensional (2-D) signal processing is presented. The applications discussed include (i) the interpolation of signals, (ii) the computation of Hilbert transform, and (iii) the complex cepstrum computation. The computational advantage of the proposed methods over the algorithms using 2-D FFT are discussed.
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    URL: http://dx.doi.org/10.1007/BF01183769
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    Efficient method for computing double matrix products (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 221-232 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We introduce an efficient method for computing matrix products of the formY=AXB, whereA andB are sparse and constant. We analyze the complexity of the method, develop quantitative criteria for determining when it can be used effectively, and demonstrate its use in a Kalman filter.
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    URL: http://dx.doi.org/10.1007/BF01183772
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    Design of 2D FIR digital filters with flatness constraints for the error function (1994)
    Springer
    Circuits, systems and signal processing 13 (1994), S. 65-75 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A method will be presented for the approximation of a desired two-dimensional frequency response by the frequency response of a two-dimensional finite-impulse-response digital filter. It is possible to match the functional values and an arbitrary number of derivatives of both responses for zero frequency, thus making the error flat up to a desired degree. Remaining degrees of freedom are used for anL 2-approximation. Closed form design formulae will be given.
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    URL: http://dx.doi.org/10.1007/BF01183841
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    An overview of median and stack filtering (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 7-45 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and “Convolute.” We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering. The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters. Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.
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    URL: http://dx.doi.org/10.1007/BF01189220
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    Convergence behavior and root signal sets of stack filters (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 171-193 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The four different types of stack filters, type-0 through type-3, are determined by four different shapes of the on-set of the positive Boolean function from which the stack filter is constructed. Under all three appending strategies commonly considered in the literature-first and last value carry-on strategy, constant value carry-on strategy, and the circular approach-stack filters of type-0 through type-2 possess the convergence property, while type-3 stack filters do not all share this property. Examples of cyclic behavior in type-3 stack filters are given. Conditions under which certain operations on stack filters which possess the convergence property produce other filters with this property are provided. In perhaps the most important result in this paper, it is shown that the root signal set of any type-3 stack filter is the intersection of the root sets of the type-1 and type-2 stack filters from which the type-3 filter is constructed. This should simplify the task of finding the set of roots of type-3 stack filters. The rates of convergence for stack filters of type-1 and type-2 are determined for each appending approach. The convergence behavior and rates of convergence of stack filters of type-1 and type-2 are then generalized to include type-1 and type-2 filters with indexi.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189226
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    Morphological pseudoconvolutions: One-parameter families of derived filters with increased invariant classes (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 195-228 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The present paper introduces a digital gray-scale morphological filtering technique that is based on postfiltering a given filter so the invariant class of the new filter is larger than the invariant class of the original filter. More specifically, the invariant class of the new filter contains the original invariant class together with all signals whose variation is below a chosen threshold. The postfiltering includes a single erosion and a single dilation by a one-parameter structuring element, the choice of parameter determining the resulting invariant class. While the methodology is quite general, the two applications considered pertain to moving averages with nonnegative weights and moving medians, both of which are morphological filters. Both suppress noise in a signal and each possesses specific advantages and disadvantages. In brief, means tend to give better noise suppression while blurring edges, whereas medians preserve edges, while at the same time flattening small background variation in the underlying signal. The new one-parameter family of filters derived from moving averages are called pseudomeans. The filters derived from medians are called pseudomedians. Both preserve uncorrupted low background variation, as well as steps. Because they preserve small variation while at the same time behaving like the original filters, both filters are especially effective when the noise occurs in bursts, rather than uniformly across the signal.
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    URL: http://dx.doi.org/10.1007/BF01189227
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