ALBERT

Note: Contents: 1 Introduction. - 1.1 Chapter Summary. - 1.2 The Meaning of the Book’s Title. - 1.3 Historical Background. - 1.4 How to Read This Book. - 1.5 Further Reading. - References. - PART 1 BASIC THEORETICAL CONCEPTS. - 2 Discrete-Time Signals and Systems. - 2.1 Chapter Summary. - 2.2 Basic Definitions and Concepts. - 2.3 Discrete-Time Signals: Sequences. - 2.3.1 Basic Sequence Operations. - 2.3.2 Basic Sequences. - 2.3.3 Deterministic and Random Signals. - 2.4 Linear Time-Invariant (LTI) Systems. - 2.4.1 Impulse Response of an LTI System and Linear Convolution. - 2.4.2 An Example of Linear Convolution. - 2.4.3 Interconnections of LTI Systems. - 2.4.4 Effects of Stability and Causality Constraints on the Impulse Response of an LTI System. - 2.4.5 Finite (FIR) and Infinite (IIR) Impulse Response Systems. - 2.4.6 Linear Constant-Coefficient Difference Equation (LCCDE). - 2.4.7 Examples of LCCDE. - 2.4.8 The Solutions of an LCCDE. - 2.4.9 From the LCCDE to the Impulse Response: Examples. - 2.4.10 Eigenvalues and Eigenfunctions of LTI Systems. - References. - 3 Transforms of Discrete-Time Signals. - 3.1 Chapter Summary. - 3.2 z-Transform. - 3.2.1 Examples of z-Transforms and Special Cases. - 3.2.2 Rational z-Transforms. - 3.2.3 Inverse z-Transform. - 3.2.4 The z-Transform on the Unit Circle. - 3.2.5 Selected z-Transform Properties. - 3.2.6 Transfer Function of an LTI System. - 3.2.7 Output Sequence of an LTI System. - 3.2.8 Zeros and Poles: Forms for Rational Transfer Functions. - 3.2.9 Inverse System. - 3.3 Discrete-Time Fourier Transform (DTFT). - 3.3.1 An Example of DTFT Converging in the Mean-Square Sense. - 3.3.2 Line Spectra. - 3.3.3 Inverse DTFT. - 3.3.4 Selected DTFT Properties. - 3.3.5 The DTFT of a Finite-Length Causal Sequence. - 3.4 Discrete Fourier Series (DFS). - 3.4.1 Selected DFS Properties. - 3.4.2 Sampling in the Frequency Domain and Aliasing in the Time Domain. - 3.5 Discrete Fourier Transform (DFT). - 3.5.1 The Inverse DFT in Terms of the Direct DFT. - 3.5.2 Zero Padding. - 3.5.3 Selected DFT Properties. - 3.5.4 Circular Convolution Versus Linear Convolution. - 3.6 Fast Fourier Transform (FFT). - 3.7 Discrete Trigonometric Expansion. - 3.8 Appendix: Mathematical Foundations of Signal Representation. - 3.8.1 Vector Spaces. - 3.8.2 Inner Product Spaces. - 3.8.3 Bases in Vector Spaces. - 3.8.4 Signal Representation by Orthogonal Bases. - 3.8.5 Signal Representation by Standard Bases. - 3.8.6 Frames and Biorthogonal Bases. - 3.8.7 Summary and Complements. - References. - 4 Sampling of Continuous-Time Signals. - 4.1 Chapter Summary. - 4.2 Sampling Theorem. - 4.3 Reconstruction of a Continuous-Time Signal from Its Samples. - 4.4 Aliasing in the Frequency Domain and Anti-Aliasing Filter. - 4.5 The Uncertainty Principle for the Analog Fourier Transform. - 4.6 Support of a Continuous-Time Signal in the Time and Frequency Domains. - 4.7 Appendix: Analog and Digital Frequency Variables. - References. - 5 Spectral Analysis of Deterministic Discrete-Time Signals. - 5.1 Chapter Summary. - 5.2 Issues in Practical Spectral Analysis. - 5.2.1 The Effect of Windowing. - 5.2.2 The Effect of Spectral Sampling. - 5.3 Classical Windows. - 5.4 The Kaiser Window. - 5.5 Energy and Power Signals and Their Spectral Representations. - 5.6 Correlation of Deterministic Discrete-Time Signals. - 5.6.1 Correlation of Energy Signals. - 5.6.2 Correlation of Power Signals. - 5.6.3 Effect of an LTI System on Correlation Properties of Input and Output Signals. - 5.7 Wiener-Khinchin Theorem. - 5.7.1 Energy Signals and Energy Spectrum. - 5.7.2 Power Signals and Power Spectrum. - References. - PART 2 DIGITAL FILTERS. - 6 Digital Filter Properties and Filtering Implementation. - 6.1 Chapter Summary. - 6.2 Frequency-Selective Filters. - 6.3 Real-Causal-Stable-Rational (RCSR) Filters. - 6.4 Amplitude Response. - 6.5 Phase Response. - 6.5.1 Phase Discontinuities and Zero-Phase Response. - 6.5.2 Linear Phase (LP). - 6.5.3 Generalized Linear Phase (GLP). - 6.5.4 Constraints on GLP Filters. - 6.6 Digital Filtering Implementation. - 6.6.1 Direct Forms. - 6.6.2 Transposed-Direct Forms. - 6.6.3 FIR Direct and Transposed-Direct Forms. - 6.6.4 Direct and Transposed-Direct Forms for LP FIR Filters. - 6.6.5 Cascade and Parallel Forms. - 6.7 Zero-Phase Filtering. - 6.8 An Incorrect Approach to Filtering. - 6.9 Filtering After Downsampling. - 6.9.1 Theory of Downsampling. - 6.9.2 An Example of Filtering After Downsampling. - References. - 7 FIR Filter Design. - 7.1 Chapter Summary. - 7.2 Design Process. - 7.3 Specifications of Digital Filters. - 7.3.1 Constraints on the Magnitude Response. - 7.3.2 Constraints on the Phase Response. - 7.4 Selection of Filter Type: IIR or FIR?. - 7.5 FIR-Filter Design Methods and Approximation Criteria. - 7.6 Properties of GLP FIR Filters. - 7.6.1 Factorization of the Zero-Phase Response. - 7.6.2 Zeros of the Transfer Function. - 7.6.3 Another Form of the Adjustable Term. - 7.7 Equiripple FIR Filter Approximations: Minimax Design. - 7.8 Predicting the Minimum Filter Order. - 7.9 MPR Algorithm. - 7.10 Properties of Equiripple FIR Filters. - 7.11 The Minimax Method for Bandpass Filters. - References. - 8 IIR Filter Design. - 8.1 Chapter Summary. - 8.2 Design Process. - 8.3 Lowpass Analog Filters. - 8.3.1 Laplace Transform. - 8.3.2 Transfer Function and Design Parameters. - 8.4 Butterworth Filters. - 8.5 Chebyshev Filters. - 8.5.1 Chebyshev-I Filters. - 8.5.2 Chebyshev-II Filters. - 8.6 Elliptic Filters. - 8.7 Normalized and Non-normalized Filters. - 8.8 Comparison Among the Four Analog Filter Types. - 8.9 From the Analog Lowpass Filter to the Digital One. - 8.9.1 Bilinear Transformation. - 8.9.2 Design Procedure. - 8.9.3 Examples. - 8.10 Frequency Transformations. - 8.10.1 From a Lowpass to a Highpass Filter. - 8.10.2 From a Lowpass to a Bandpass Filter. - 8.10.3 From a Lowpass to a Bandstop Filter . - 8.11 Direct Design of IIR Filters. - 8.12 Appendix. - 8.12.1 Trigonometric Functions with Complex Argument. - 8.12.2 Elliptic Integrals. - 8.12.3 Jacobi Elliptic Functions. - 8.12.4 Landen-Gauss Transformation. - 8.12.5 Elliptic Rational Function. - References. - PART 3 SPECTRAL ANALYSIS. - 9 Statistical Approach to Signal Analysis. - 9.1 Chapter Summary. - 9.2 Preliminary Considerations. - 9.3 Random Variables. - 9.4 Ensemble Averages. - 9.5 Stationary Random Processes and Signals. - 9.6 Ergodicity. - 9.7 Wiener-Khinchin Theorem for Random Signals and Power Spectrum. - 9.8 Cross-Power Spectrum of Two Random Signals. - 9.9 Effect of an LTI System on a Random Signal. - 9.10 Estimation of the Averages of Ergodic Stationary Signals. - 9.10.1 General Concepts in Estimation Theory. - 9.10.2 Mean and Variance Estimation. - 9.10.3 Autocovariance Estimation. - 9.10.4 Cross-Covariance Estimation. - 9.11 Appendix: A Road Map to the Analysis of a Data Record. - References. - 10 Non-Parametric Spectral Methods. - 10.1 Chapter Summary. - 10.2 Power Spectrum Estimation. - 10.3 Periodogram. - 10.3.1 Bias. - 10.3.2 Variance. - 10.3.3 Examples. - 10.3.4 Variance Reduction by Band- and Ensemble-Averaging. - 10.4 Bartlett’s Method. - 10.5 Modified Periodogram. - 10.6 Welch’s Method. - 10.7 Blackman-Tukey Method. - 10.8 Statistical Significance of Spectral Peaks. - 10.9 MultiTaper Method. - 10.10 Estimation of the Cross-Power Spectrum of Two Random Signals. - 10.11 Use of the FFT in Power Spectrum Estimation. - 10.12 Power Spectrum Normalization. - References. - 11 Parametric Spectral Methods. - 11.1 Chapter Summary. - 11.2 Signals with Rational Spectra . - 11.3 Stochastic Models and Processes. - 11.3.1 Autoregressive-Moving Average (ARMA) Model. - 11.3.2 Autoregressive (AR) Model. - 11.3.3 Moving Average (MA) Model. - 11.3.4 How the AR and MA Modeling Approaches Are Theoretically Related. - 11.3.5 First-Order AR and MA Models: White, Red and Blue Noise. - 11.3.6 Higher-Order AR Models. - 11.4 The AR Approach to Spectral Estimation. - 11.5 AR Modeling and Linear Prediction. - 11.6