Synthesis and implementation of recursive linear shift-variant digital filters

TLDR: This paper proposes two techniques to approximate a given impulse response as a degenerate sequence that is realizable as a recursive difference equation and uses a least squares error criterion to minimize the difference between the given and the approximated impulse responses.

Abstract: In this paper, problems associated with the synthesis and implementation of recursive linear shift-variant digital filters are investigated. We propose two techniques to approximate a given impulse response as a degenerate sequence that is realizable as a recursive difference equation. Both techniques use a least squares error criterion to minimize the difference between the given and the approximated impulse responses. Numerical examples illustrating and comparing the results of these techniques are included. In addition, we present several recursive structures for the implementation of both causal and noncausal degenerate impulse responses.