Least-squares design of FIR filters as a tapped cascaded interconnection of substructures

Least-squares design of FIR filters is considered for a structure consisting of a tapped cascaded interconnection of identical subfilters. By using computationally efficient substructures, savings are achieved in the number of multiplications, as compared to direct form designs of comparable integrated squared error. Analytical formulas are derived for the optimum tap coefficients, based on the time-domain composition of the overall impulse response. Examples of linear-phase lowpass and bandpass filter design are given.