DCGA optimization of lowpass FRM IIR digital filters over CSD multiplier coefficient space

Abstract

Frequency-Response Masking (FRM) technique is known to significantly reduce computational complexity of sharp transition-band digital filters. This paper presents a novel technique for the design and optimization of a guaranteed BIBO stable FRM IIR lowpass digital filter, employing an odd-order IIR elliptic minimum Q-factor (EMQF) prototype digital filter. The bilinear-LDI design approach is used to realize the prototype digital filter as a parallel combination of a pair of digital allpass networks. A diversity-controlled genetic algorithm (DCGA) is employed for the optimization of the bilinear-LDI FRM IIR digital filter over the canonical signed-digit multiplier coefficient space. A LUT-based scheme is employed to ensure that the resulting FRM IIR digital filter is automatically BIBO stable during DCGA optimization. The proposed technique is illustrated through its application to the optimization of a fifth-order lowpass elliptic FRM IIR digital filter, resulting in a rapid convergence speed of around 300 iterations.