ISSN:
1573-2878
Keywords:
Digital filters
;
finite impulse response
;
frequency sampling
;
Lagrange multiplier optimization
;
interpolation
;
discrete Fourier transform
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00940581
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