Weighted least-squares design of variable 1-D FIR filters with arbitrary magnitude responses

Variable digital filters with variable cut-off frequencies can be designed by frequency transformation methods. Such methods are simple, but they are not applicable to the design of variable fitters with arbitrarily variable frequency responses. This paper proposes an efficient method for designing variable 1-D FIR digital filters with arbitrarily variable magnitude characteristics with linear phase. First, each coefficient of the variable FIR filter is assumed to be a m dimensional (M-D) polynomial of the spectral parameters that specify different variable magnitude characteristics. Then a least-squares algorithm is presented for finding the optimal polynomial coefficients by minimizing the weighted squared error between the desired and the actual variable frequency response. The proposed approach can be easily extended for designing variable FIR filters with nonlinear phase.