A unified approach for optimal design of FIR filters with arbitrary frequency response

A unified approach for the optimal design of finite-impulse response (FIR) filters with arbitrary´ magnitude and phase response using second-order cone programming (SOCP) is proposed. FIR filters with desired frequency response can be implemented by minimizing the frequency domain response error measure (L₁, L₂, or L_∞-norm of the error) between the designed filter response and the desired one. 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 SOCP and solved efficiently via the well-established interior point method. The SOCP approach allows much more design flexibility in comparison to the classical minimax, least-square, and eigenfilter approaches. Computer simulation results for the design of FIR filters with desired frequency response show good performance of the proposed approach.