The Nehari shuffle: FIR(q) filter design with guaranteed error bounds

1 January 1992

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing

Vol. 40 (8) , 1876-1883
https://doi.org/10.1109/78.149990

Abstract

An approach to the problem of designing a finite impulse response filter of specified length q which approximates in uniform frequency (L∞) norm a given desired (possibly infinite impulse response) causal, stable filter transfer function is presented. An algorithm-independent lower bound on the achievable approximation error is derived, and an approximation method that involves the solution of a fixed number of all-pass (Nehari) extension problems (and is therefore called the Nehari shuffle) is presented. Upper and lower bounds on the approximation error are derived for the algorithm. Examples indicate that the method closely approaches the derived global lower bound. The method is compared with the Preuss (complex Remez exchange) algorithm in some examples

Keywords

This publication has 10 references indexed in Scilit:

Complex Chebyshev approximation for FIR digital filters
IEEE Transactions on Signal Processing, 1991
On the design of FIR filters by complex Chebyshev approximation
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques
IEEE ASSP Magazine, 1987
Design of FIR filters in the complex domain
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1987
On model reduction
Published by Institute of Electrical and Electronics Engineers (IEEE) ,1986
All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
International Journal of Control, 1984
Principal component analysis in linear systems: Controllability, observability, and model reduction
IEEE Transactions on Automatic Control, 1981
Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase
IEEE Transactions on Circuit Theory, 1972
ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
Mathematics of the USSR-Sbornik, 1971
On Bounded Bilinear Forms
Annals of Mathematics, 1957