A unified framework for designing FIR filters with arbitrary magnitude and phase response

A unified framework for the optimal design of finite impulse response (FIR) filters with arbitrary magnitude and phase response using second-order cone (SOC) programming is proposed. FIR filters with desired frequency response can be implemented by minimizing the frequency domain response error measure (L ₁, L₂, or L_∞ norm of the error) between the desired response and the designed filter response. Some constraints can also be imposed in the passband or/and stopband to satisfy applications-oriented requirements. These optimal design problems can be reformulated as convex optimization form as the second-order cone programming and solved efficiently via the well-established interior point method. The SOC programming approach allows much more design flexibility in comparison to the classical minimax, least-square, and eigenfilter approaches. Computer simulations are presented to illustrate the developed algorithms and to evaluate the design performance. Simulation results for the design of fractional delay FIR filters and filters with desired frequency response show good performance of the proposed methods.