Variants of Genetic Algorithm for Efficient Design of Multiplier-Less Finite Impulse Response Digital Filter

Digital Signal Processing (DSP) is one of the most powerful technologies which have given appropriate shape to science, engineering and technology of twenty-first century. It has already found its significant applications in various areas like communication, medical imaging, speech and video processing, military surveillance, and so on. A perfect blending of sophisticated algorithms, powerful mathematical operations and specialized techniques has made this technological revolution to happen. As a matter of fact, DSP has become an inevitable part of modern technology in no times. Digital filters are basic building blocks of any digital signal processing system of practical importance. Flexibility in the design of such filters has given the DSP techniques an extra edge over other alternatives. Entire set of digital filters are broadly categorized into Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters regardless of their frequency domain specifications. This classification is actually carried out on the basis of the internal architecture of the concerned filter. In comparison with its IIR counterparts, FIR filters are having desirable features like guaranteed stability, linear phase response and low coefficient sensitivity which have made this filter so popular for most of the wireless applications (Mitra, 2006). However, non-recursive FIR filters are heavily challenged by recursive IIR filters as it needs large number of arithmetic operations during its implementation. This in turn, limits the speed of the filter and consumes more power which makes it inappropriate for use in portable wireless devices like mobile phones, laptops, etc. During implementation on high speed digital computer or DSP chips, each coefficient of digital filters is stored in registers of finite length and subsequently mathematical operations are performed by means of adders and multipliers. Considerable attention and effort have already been made by many of the researchers towards the design of low-power FIR filters. One of the most convenient ways to design such filters has been achieved by restricting each coefficient as sum of signed powers of two (SPT) terms. However, such restriction implicitly signifies that the coefficient space is bounded and limited by the coefficient word-length. This kind of representation substitutes the multiplication operation by simple addition and data shifting operation and finally leads multiplier-less hardware. This article throws sufficient light on the design of power of two (POT) FIR filter exclusively. In connection to this, the design strategy has been regarded as an optimization problem because of the proper tuning of several interdependent parameters. A special class of evolutionary optimization algorithm, namely Genetic Algorithm (GA) along with some of its recent variants, has been taken into special consideration. Performances of the designed filters, as achieved with different algorithms, have been illustrated and properly analyzed. Towards the end of the article, directions for future research have been rightly pointed out.