This paper presents a novel diversity-controlled (DC) genetic algorithm (GA) for the design and rapid optimization of frequency-response masking (FRM) digital filters over the CSD multiplier coefficient space. The resulting FRM digital filters incorporate bilinear-LDI IIR interpolation subfilters realized as a parallel combination of a pair of allpass digital networks. A novel LUT scheme is developed to ensure that the FRM digital filters under consideration are automatically BIBO stable throughout the course of DCGA optimization. The salient feature of the proposed LUT scheme is that it makes no recourse to slack variables for referencing the values of the CSD multiplier coefficients. The DCGA optimization fitness function includes not only the magnitude but also the group-delay frequency-response of FRM digital filters so as to minimize phase distortion caused by the IIR interpolation subfilters. An example is given to illustrate the application of the proposed DCGA optimization to the design of a lowpass FRM digital filter incorporating a seventh-order bilinear-LDI interpolation subfilter.

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<p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span style="font-family: NimbusRomNo9L-Medi; font-size: 9pt; mso-bidi-font-family: NimbusRomNo9L-Medi;"><span style="font-family: Times New Roman;">This paper presents a novel diversity-controlled (DC) genetic algorithm (GA) for the optimization of digital Intermediate Frequency (IF) filters over the (finite-precision) canonical signed-digit (CSD) multiplier coefficient space. This optimization exploits the bilinear-lossless-discrete- integrator (bilinear-LDI) lattice digital filter design approach for the realization of the required infinite-precision seed digital IF filter chromosome. A look-up table (LUT) approach is proposed to ensure that the finite-precision CSD digital IF filter chromosomes generated in the course of DCGA optimization are guaranteed to be bounded-input bounded-output (BIBO) stable. The salient feature of DCGA optimization is that it permits external control over the population diversity (i.e. the parent selection pressure) to achieve a high convergence speed. This feature is illustrated through the application of the proposed DCGA optimization to the design of a pair of practical digital IF filters satisfying different design specifications. It is observed that, for both digital IF filter designs, the DCGA optimization results in around an order of magnitude improvement in the convergence speed as compared to a conventional GA optimization.</span></span></p>

This work is concerned with the development of a novel diversity-controlled (DC) genetic algorithm (GA) for the design and rapid optimization of frequency-response masking (FRM) digital filters incorporating bilinear lossless discrete-integrator (LDI) IIR interpolation sub-filters. The selection of FRM approach is inspired by the fact it lends itself to the design of practical sharp-transition band digital filters in terms of gradual-transition band FIR interpolation sub-filters. The proposed DCGA optimization is carried out over the canonical-signed-digit (CSD) multiplier coefficient space, resulting in FRM digital filters which are capable of direct implementation in digital hardware. A novel CSD look-up table (LUT) scheme is developed so that in every stage of DCGA optimization, the IIR interpolation sub-filters constituent in the intermediate and final FRM digital filters are guaranteed to be automatically BIBO stable. The proposed DCGA optimization permits simultaneous optimization of the magnitude-frequency as well of the group-delay frequency response of the desired FRM digital filters. An example is given to illustrate the application of the resulting DCGA optimization to the design of a lowpass FRM digital filter incorporating a fifth-order bilinear-LDI interpolation subfilter.

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