Abstract
An optimization method is proposed for the design of high-order all-pass delay equalizers for a prescribed group-delay characteristic by using the cascade form realization of digital filters. Unlike other methods, in the proposed method stability is guaranteed by imposing certain mild constraints on the filter coefficients so that the unconstrained optimization technique of Fletcher and Powell is used. To reduce the function minimization time, design values of the parameters of the delay equalizers, obtained by Bernhardt's simplified method, are used as the initial vector in the optimization technique of the proposed method. It is shown that the proposed method for the design of optimal delay equalizers results in all classes of equalizers with real and complex poles and approximates the prescribed group delay more accurately.
Similar content being viewed by others
References
A. Bernhardt, Simplified design of high-order recursive group-delay filters,IEEE Trans. Acoust. Speech Signal Process.,28, 498–503, 1980.
A. G. Deczky, Synthesis of recursive digital filters using the minimump-error criteria,IEEE Trans. Audio Electroacoust.,20, 257–263, 1972.
A. G. Deczky, Recursive digital filters having equiripple group delay,IEEE Trans. Circuits and Systems,21, 131–134, 1974.
R. Fletcher and M. J. D. Powell, A rapidly convergent descent method for minimization,Comput. J.,6, 163–168, 1963.
G. A. Maria and M. M. Fahmy, 1p approximation of the group delay response of one- and two-dimensional filters,IEEE Trans. Circuits and Systems,21, 431–436, 1974.
G. A. Maria and M. M. Fahmy, An 1p design technique for two-dimensional digital recursive filters,IEEE Trans. Acoust. Speech Signal Process.,22, 15–21, 1974.
K. P. Prasad, Computer-aided analysis and design of one- and two-dimensional digital filters, Ph.D Thesis, Indian Institute of Technology, Madras, 1978.
K. P. Prasad and P. S. Reddy, Method for designing stable 2-D digital filters,Electron Lett. 13 (13), 385–386, 1977.
Programmer's Manual, System/360 Scientific Subroutine Package (360-CM-03X) Version III, Document H20-0205-3, IBM Data Proc. Div., White Plains, NY, 1968.
Author information
Authors and Affiliations
Additional information
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739.
Rights and permissions
About this article
Cite this article
Reddy, P.S., Ganapathy, V. & Swamy, M.N.S. Modified design of high-order 1-D all-pass recursive digital filters. Circuits Systems and Signal Process 8, 445–453 (1989). https://doi.org/10.1007/BF01599766
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01599766