A matrix-based constrained minimax design of 2-D FIR filters with reduced group delay error

Conventional algorithms for phase-error constrained minimax (PCMM) designs of two-dimensional (2-D) FIR filters vectorize the filter´s impulse response coefficient. Recently, an efficient algorithm exploiting the matrix nature of the impulse response is proposed for the constrained least-squares (CLS) design of 2-D nonlinear-phase FIR filters. This paper devotes to transform the PCMM design into the same form as the CLS design. A 2-D sigmoid function is introduced to constrain the phase error, resulting in 2-D FIR filters with much smaller maximum group delay error than that obtained under corresponding constant phase-error constraints. Design example and comparisons demonstrate the effectiveness and high efficiency of the proposed method.