Finite-time-domain synthesis of recursive linear time-variant causal digital filters by separable sequences

Abstract

Linear time-variant (LTV) digital filters whose impulse responses are separable sequences have been proved to be recursive. Such filters have the potential in saving computation time and storage. This paper presents a method to synthesize a desired LTV digital filter given in numerical form in a finite time domain by a separable sequence of a given order. The method finds the separate sequence by alternately using two nonlinear restrictions that an optimal recursive LTV filter approximating the desired filter must satisfy. The performance of the proposed method is illustrated and compared with other available ones through numerical examples. The results of the comparisons show that our method provides smaller synthesis errors than the others.