Journal of Signal and Information Processing, 2012, 3, 344-351 http://dx.doi.org/10.4236/jsip.2012.33044 Published Online August 2012 (http://www.SciRP.org/journal/jsip) Design of Sharp 2D Multiplier-Less Circularly Symmetric FIR Filter Using Harmony Search Algorithm and Frequency Transformation Manju Manuel, Elizabeth Elias Department of Electronics and Communication Engineering, National Institute of Technology, Calicut, Kerala, India. Email: manju.manuel@gmail.com, elizabeth@nitc.a.c.in Received March 31 st , 2012; revised April 29 th , 2012; accepted May 11 th , 2012 ABSTRACT In this paper, we present a novel and efficient method for the design of a sharp, two dimensional (2D) wideband, circu- larly 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 Algo- rithm (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 multi- plier-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 pro- posed discrete optimization using modified HSA can be used to solve optimization problems in other engineering disci- plines, where the search space consists of integers. Keywords: Two Dimensional Filter; Frequency Response Masking; Harmony Search Algorithm; T1 and T2 Transformations; Canonic Signed Digit Representation 1. Introduction Frequency Response Masking (FRM) is a much ac- claimed technique to synthesize sharp linear phase 1D FIR filters with sparse coefficients [1]. The prominent feature of this approach is that the sparse filter coefficients results in fewer number of multipliers and better saving of power. This enormous computational saving by this ap- proach compared to the traditional mini-max approach has resulted in the deployment of the FRM technique in a wide variety of applications like software defined radio, array beam-forming, filter-banks, FPGA implementations etc [2]. The computational complexity can be brought down further, if the coefficients of the FRM filter are represented in the SPT space [3]. Regarding the imple- mentation of a digital filter, since multipliers are the most computationally intensive blocks, replacing them by shifters and adders will result in the saving of the com- putation time as well as chip area. It is also known that if subtractions are also used to carry out multiplication, the number of SPT terms can further be minimized as in the case of the Canonic Signed Digit Representation [4]. Direct rounding of the filter coefficients to the CSD space, causes degradation in the filter performance. This necessitates the use of a suitable optimization technique filter in the discrete space with the required specifications. Since the search space is discrete, the conventional gra- dient based approaches cannot be employed. In this con- text, the meta-heuristic optimization algorithm is a good alternative, since it is capable of generating optimal solu- tions in a multimodal, multidimensional search space. A multiplier-less FRM FIR filter was designed in the CSD space using the Genetic Algorithm (GA) in [3]. Besides, GA was used to design a 2D filter in [5]. The problem associated with GA is the slow convergence speed [6]. Genetic algorithm was modified in [7] and used for the design of 1D FRM FIR filter. But enormous computa- tional time was required for this approach. Therefore, we propose an efficient technique for the design of FRM filter in the CSD space using the modified Harmony Search Algorithm with reduced computation time as well as good Copyright © 2012 SciRes. JSIP