Faculty Bibliography

This paper describes a new class of nonsymmetric maximally flat low-pass finite impulse response (FIR) filters, By subjecting the magnitude and group delay responses (individually) to differing numbers of flatness constraints, the new filters are obtained, It is found that these filters achieve a smaller delay than symmetric filters while maintaining relatively constant group delay around omega = 0, with no degradation of the frequency response magnitude, The design of these filters is initially investigated using Grobner bases, An analytic design technique, applicable to a subset of the forgoing filters, is provided that does not depend on Grobner basis computations.

This brief describes an exchange algorithm for the frequency domain design of linear-phase FIR equiripple filters where the Chebyshev error in each band is specified. The algorithm is a hybrid of the algorithm of Hofstetter, Oppenheim and Siegel and the Parks-McClellan algorithm. The brief also describes a modification of the Parks-McClellan algorithm where either the passband or the stopband ripple size is specified and the other is minimized.

This brief describes a modification of a technique proposed by Vaidyanathan for the design of filters having Bat passbands and equiripple stopbands. The modification ensures that the passband is monotonic and does so without the use of concavity constraints. Another modification described in this brief adapts the method of Vaidyanathan to the design of low-pass differentiators having a specified degree of tangency at omega = 0.

We consider the design of 2-D linear phase finite impulse response (FIR) filters according to the least squares (LS) error criterion subject to equality and/or inequality constraints, Since we use a frequency domain formulation, these constraints can be used to explicitly prescribe (frequency-dependent) error tolerances, the maximum, minimum, or fixed values of the frequency response at certain points and/or regions. Our method combines Lagrange multiplier and Kuhn-Tucker theory to solve a much wider class of problems than do standard methods, It allows arbitrary compromises between the LS and the equiripple design.

We describe a set of programs for circular convolution and prime length fast Fourier transforms (FFT's) that are relatively short, possess great structure, share many computational procedures, and cover a large variety of lengths, The programs make clear the structure of the algorithms and clearly enumerate independent computational branches that can be performed in parallel, Moreover, each of these independent operations is made up of a sequence of suboperations that can be implemented as vector/parallel operations, This is in contrast with previously existing programs for prime length FFT's: They consist of straight line code, no code is shared between them, and they cannot be easily adapted for vector/parallel implementations. We have also developed a program that automatically generates these programs for prime length FFT's, This code-generating program requires information only about a set of modules for computing cyclotomic convolutions.