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. 12341245. ISSN 00984094. http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetcs85k

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Abstract
Lattice structures are developed for the realization ofminputpoutput discretetime allpass transfer matricesH(z), given in the form of a right matrixfraction 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 twopair 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 twopairs separated by vector delays, with each twopair being a multiinput multioutput 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 cascadedlattice 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 wellknown GrayMarkel 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 cascadedmultivariable lattice structures.
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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 8218310, in part by CALTECH’s Programs in Advanced Technology Grant, and in part by the National Science Foundation under Grant ECS 8404245. 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. 
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