Approximation Methods in Multidimensional Filter Design and Related Problems Encountered in Multidimensional System Design.

摘要

The research conducted contributes towards the development of a theory to analyze and design linear shift-invariant multivariable multidimensional discrete and continuous systems. Recursive schemes to compute rational approximants to a power series in two variables having constant matrices for coefficients are developed. Approximants to special matrix power series are investigated and the properties of these approximants are delineated in a strictly mathematical setting and their implications are interpreted via physical reasonings. Algebraic procedures to tet thee approximants for stability are provided, and criteria for guaranteeing the invariance of properties like positivity and stability under parameter changes or perturbation are advanced. Attention is directed throughout towards the reduction of algebraic computational complexity. In the important problem of filter stabilization without appreciable change in the magnitude of the frequency response, recent results on multiplicative computational complexity theory is exploited to demonstrate the feasibility of implementing efficiently a 2-D discrete Hilbert transform. Criteria for 2-D rational approximants to be maximally flat are obtained.