Design of Sharp 2D Multiplier-Less Circularly Symmetric FIR Filter Using Harmony Search Algorithm and Frequency Transformation

Abstract

In this paper, we present a novel and efficient method for the design of a sharp, two dimensional (2D) wideband, circularly symmetric, FIR filter. First of all, a sharp one dimensional (1D) infinite precision FIR filter is designed using the Frequency Response Masking (FRM) technique. This filter is converted into a multiplier-less filter by representing it in the Canonic Signed Digit (CSD) space. The design of the FRM filter in the CSD space calls for the use of a discrete optimization technique. To this end, a new optimization approach is proposed using a modified Harmony Search Algorithm (HSA). HSA is modified in such a way that, in every exploitation and exploration phase, the candidate solutions turns out to be integers. The 1D FRM multiplier-less filter, is in turn transformed to the 2D equivalent using the recently proposed multiplier-less transformations namely, T1 and T2. These transformations are successful in generating circular contours even for wideband filters. Since multipliers are the most power consuming elements in a 2D filter, the multiplier-less realization calls for reduced power consumption as well as computation time. Significant reduction in the computational complexity and computation time are the highlights of our proposed design technique. Besides, the proposed discrete optimization using modified HSA can be used to solve optimization problems in other engineering disciplines, where the search space consists of integers.