General Structural Representations for Multi-Input Multi-Output Discrete-Time FIR and IIR Lossless Systems

Citation

Doğanata, Zinnur (1990) General Structural Representations for Multi-Input Multi-Output Discrete-Time FIR and IIR Lossless Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/h011-7b66. https://resolver.caltech.edu/CaltechETD:etd-02222007-083438

Abstract

Discrete-time lossless systems have been found to be of great importance in many signal processing applications. However, a representation for lossless transfer matrices that spans all such matrices with the smallest possible number of parameters has not been proposed earlier. Existing representations are usually for special cases and therefore not general enough. In this study, two general and minimal representations are presented for multi-input, multi-output FIR and IIR lossless systems. The first representation is in terms of planar rotations and it leads to multi-input, multi-output lattice structures. The second representation is in terms of unit-norm vectors and it enables shorter convergence times in optimization applications. A simple modification of this representation leads to structures that remain lossless under quantization. The structures that follow from these representations share some properties such as the orthogonality of the implementations, and minimality of the number of parameters and scalar delays they are. Since all lossless transfer matrices can be spanned by appropriately adjusting their parameters, these structures can be particularly useful in applications that involve optimization under the constraint of losslessness. Some examples of such applications are included.

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