A general family of multivariable digital lattice filters

Lattice structures are developed for the realization of -input -output discrete-time all-pass transfer matrices , given in the form of a right matrix-fraction description . 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 . 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 when gives rise to the well-known Gray-Markel digital lattice structures, whereas another special case with and leads 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.