A Novel Discrete Particle Swarm Optimization for FRM FIR Digital Filters

Abstract

This paper presents a novel discrete particle swarm optimization (PSO) for frequency response masking (FRM) finite impulse response (FIR) digital filters over the canonical signed-digit (CSD) multiplier coefficient space. A look-up table (LUT) scheme is employed to ensure that the PSO automatically searches through permissible CSD multiplier coefficient values in the course of optimization without any recourse to backtracking. This is achieved by searching through the indices of the CSD multiplier coefficient values in the LUT instead of the coefficient values themselves. In this way, the resulting multiplier coefficient values are ensured to conform to a prespecified wordlength as well as to a prespecified maximum number of non-zero digits. The salient feature of this LUT scheme is that by introducing barren layers in the LUT, there is no need to limit the search space manually in the course of PSO to prevent from going over the boundaries of the search space. Examples are given to illustrate the application of the proposed PSO to the design and optimization of a lowpass and a bandpass FRM FIR digital filters

High-speed multiplierless Frequency Response Masking (FRM) FIR filters with reduced usage of hardware resources

“…[1]- [2], [7]- [12]. Since the transposed structure of a FIR filter has a low critical path, it would be convenient to use this structure in all the subfilters [7]- [12].…”

“…In this sense, and in order to couple with FRM-based design methods such as [7]- [8], we recommend the canonical representation (CSD).…”

“…A distinct option is to use method [6] for the joint design of the FRM subfilters directly in the integer-coefficients space and then the reduction of the number of adders can be applied individually to every subfilter using either GE or CSE eliminations. Another approach has been proposed in [7]- [8], where all the subfilters are jointly optimized in the Canonical Signed Digit (CSD) space. Then, a CSE-based reduction of adders can be used in every subfilter.…”