Constrained least square design of FIR filters with arbitrary magnitude and phase responses

This paper presents an efficient multiple exchange algorithm for the frequency domain design of digital FIR filters with arbitrary magnitude and phase responses. The designed filters minimize the L-2 norm of the weighted complex frequency domain error function subject to constraints on the resulting magnitude and phase errors. This general design criterion allows for an arbitrary trade-off between complex L-2 approximation and Chebyshev approximation of given magnitude and phase responses. The optimization problem is solved by iteratively solving small quadratic programs. These linearly constrained subproblems can be solved using robust standard software.