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Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters

Liu, Vincent C. and Vaidyanathan, P. P. (1988) Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters. IEEE Transactions on Circuits and Systems, 35 (6). pp. 625-635. ISSN 0098-4094. http://resolver.caltech.edu/CaltechAUTHORS:LIUieeetcs88

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Abstract

Normal-form fixed-point state-space realization of IIR (infinite-impulse response) filters are known to be free from both overflow oscillations and roundoff limit cycles, provided magnitude truncation arithmetic is used together with two's-complement overflow features. Two normal-form realizations are derived that utilize circulant and skew-circulant matrices as their state transition matrices. The advantage of these realizations is that the A-matrix has only N (rather than N2) distinct elements and is amenable to efficient memory-oriented implementation. The problem of scaling the internal signals in these structures is addressed, and it is shown that an approximate solution can be obtained through a numerical optimization method. Several numerical examples are included.


Item Type:Article
Additional Information:© Copyright 1988 IEEE. Reprinted with permission. Manuscript received August 29, 1985; revised May 5, 1986 and July 22, 1987. This work was supported in part by the National Science Foundation under Grant ECS 84-04245 and in part by Caltech’s programs in advanced technology sponsored by Aerojet General, General Motors, GTE, and TRW. V.C. Liu was under a Schlumberger Fellowship for the period during which this work was performed. This paper was recommended by Associate Editor A. N. Venetsanopoulos.
Subject Keywords:digital arithmetic; digital filters; matrix algebra; sensitivity analysis; state-space methods
Record Number:CaltechAUTHORS:LIUieeetcs88
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LIUieeetcs88
Alternative URL:http://dx.doi.org/10.1109/31.1800
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5900
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:08 Nov 2006
Last Modified:26 Dec 2012 09:16

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