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A general family of multivariable digital lattice filters

Vaidyanathan, P. P. and Mitra, Sanjit K. (1985) A general family of multivariable digital lattice filters. IEEE Transactions on Circuits and Systems, 32 (12). pp. 1234-1245. ISSN 0098-4094.

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Lattice structures are developed for the realization ofm-inputp-output discrete-time all-pass transfer matricesH(z), given in the form of a right matrix-fraction description(MFD): H(z)=N(z)D^{-l}(z). The procedure is based on the generation of a sequence of all pass matrices of successively decreasing order, by matrix LBR two-pair extraction. Two cases are distinguished: the first case is when none of the intermediate allpass matrices is degenerate. For this case, the resulting structures are in the form of a cascade of matrix two-pairs separated by vector delays, with each two-pair being a multi-input multi-output digital filter structure characterized by an orthogonal transfer matrix of dimension(m + p) times ( m + p). The structures are in general either completely controllable or completely observable, depending upon the location of the delay elements. The synthesis technique also leads to a procedure for obtaining the greatest common right divisor between the polynomial matrices involved in the MFD. The results are extended to the cascaded-lattice synthesis of arbitrary stable transfer matrices by an embedding process. The developments of this paper automatically place in evidence a procedure for testing the stability of a transfer matrix. A special case of the resulting structures whenp = m =1gives rise to the well-known Gray-Markel digital lattice structures, whereas another special case withp = 2andm = 1leads to certain recently reported orthogonal digital filters. The second case, where some of the intermediate allpass matrices are degenerate, is handled separately, leading to a modified form of cascaded-multivariable lattice structures.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1985 IEEE. Reprinted with permission. Manuscript received November 22, 1984; revised July 17, 1985. This work was supported in part by the National Science Foundation under Grant ECS 82-18310, in part by CALTECH’s Programs in Advanced Technology Grant, and in part by the National Science Foundation under Grant ECS 84-04245. We wish to express our appreciation to Reviewer #2, who not only pointed out some important references, but also suggested a number of very valuable improvements to the manuscript.
Issue or Number:12
Record Number:CaltechAUTHORS:VAIieeetcs85k
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5862
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Deposited On:06 Nov 2006
Last Modified:09 Mar 2020 13:19

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