Weighted least-squares method for designing arbitrarily variable 1-D FIR digital filters

Abstract

Variable digital filters with variable cutoff frequencies can be designed by frequency transformation methods. Such methods are simple, but they are not applicable to the design of variable filters with arbitrarily variable frequency responses. This paper proposes an efficient method for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with arbitrarily variable magnitude characteristics and specified linear or nonlinear phase responses. First, each coefficient of the variable FIR filter is assumed to be a multi-dimensional (M-D) polynomial of spectral parameters that specify different variable magnitude characteristics. Then we present a pair of least-squares algorithms for finding the optimal polynomial coefficients by minimizing the weighted squared error between the desired variable frequency response and the actual frequency response. The first one is for designing 1-D FIR filters with variable magnitude response and linear-phase, and the second one is for designing variable 1-D FIR filters with variable magnitude response and nonlinear-phase. Although the first algorithm can be regarded as a special case of the second one, using the first one in the linear case can simplify the design significantly. The proposed methods are very straightforward and efficient for designing variable digital filters with arbitrarily variable magnitude responses and specified linear or nonlinear phases.