On sequential refinement schemes for recursive digital filter design

Abstract

A linear synthesis technique is developed for a recursive digital filter which approximates the desired discrete impulse response. Sequential schemes which can be used to refine the preliminary filter design are developed for three distinct cases in which the output sequence number, the filter order, and the number of the numerator coefficients of the transfer function are allowed to vary separately. By use of matrix inversion lemmas, the new sets of filter coefficients are obtained sequentially based on the old estimates and the new data without having to repeat the entire design procedure.