Low Pass Fir Filter Design using Genetic Algorithm

IJSTE - International Journal of Science Technology & Engineering | Volume 3 | Issue 06 | December 2016 ISSN (online): 2349-784X

Low Pass FIR Filter Design using Genetic Algorithm Surabhi Chaturvedi Department of Electronics & Telecommunication Engineering CSIT, Durg, India

Navneet Kumar Sahu Department of Electronics & Telecommunication Engineering CSIT, Durg, India

Abstract Filtering is a class of signal processing, which defines the feature of filters which performs the complete suppression of some aspect of the signal. Digital filters are used in numerous applications from control systems, systems for audio and video processing, and communication systems and for medical applications. Digital filtering can be used to produce very low frequency signals, such as those occurring in biomedical and seismic applications very efficiently. The FIR filter has two major advantages of stability and linear phase, and has been widely used in different applications. An efficient design algorithm for low pass FIR filter design has been presented in this paper which is genetic algorithm. This algorithm provides the flexibility in control of various parameters such as population size, number of generations, crossover probability and so on.

Keywords: FIR (Finite Impulse Response), GA (Genetic Algorithm) ________________________________________________________________________________________________________ I.

INTRODUCTION

Nowadays digital filters can be used to perform many filtering tasks and replacing traditional role of analog filters. Digital filter is very important tool in digital signal processing field. This is used for the separation of signals that have been combined and the restoration of signals that have been distorted by some way [5]. FIR filters are often used in many phase-sensitive applications because they can always be designed to have linear phase. They are inherently stable due to its poles which lie at the origin.

Genetic algorithm optimization methods have emerged as a powerful approach for solving the more difficult optimization problems [3]. As a stochastic algorithm, GA can be used to solve complicated problem with a huge search space, the discrete search space is partitioned into smaller ones. Each of the small space is constructed surrounding an optimum continuous solution with a floating pass band gain.

II. GENETIC ALGORITHM Genetic Algorithms (GAs) are adaptive heuristic search algorithms introduced on the evolutionary themes of natural selection.

The fundamental concept of the GA design is to model processes in a natural system that is required for evolution, specifically those that follow the principles proposed by Charles Darwin to find the survival of the fittest [8]. Genetic Algorithm is a robust and efficient optimization procedure which finds the global optimal solution for many applications. After initializing the first generation population of the chromosome, some individuals in the existing population will be selected according to a certain selection mechanism. Those selected individuals are called "parents" and they will produce "children" by crossover and mutation operators [4]. The generation process containing selection, crossover and mutation will be repeated until certain termination criteria have been reached. Best fitted chromosomes, called elite chromosomes are transmitted as it is to the next generation.

With each generation, better solutions are obtained [6]. The genetic algorithm comprises three genetic operations reproduction, crossover and mutation; these three operations are applied again and again, starting from an initial population of individuals.

Only good individuals remain in the population and reproduce, while the bad individuals are eliminated from the population finally, the population will consist only of the best individuals fulfilling the design specification.

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Low Pass FIR Filter Design using Genetic Algorithm (IJSTE/ Volume 3 / Issue 06 / 017)

Fig. 1: Flow Chart of Genetic Algorithm

III. RESULTS

Fig. 2: Magnitude Response of Low Pass FIR Filter with

and without GA

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Low Pass FIR Filter Design using Genetic Algorithm (IJSTE/ Volume 3 / Issue 06 / 017)

Fig. 3: Phase Response of Low Pass FIR Filter with and without GA

Fig. 4: Step Response of Low Pass FIR Filter with and without GA

Fig. 5: Impulse Response of Low Pass FIR Filter with and without GA

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Low Pass FIR Filter Design using Genetic Algorithm (IJSTE/ Volume 3 / Issue 06 / 017)

Fig. 6: Pole Zero Plot of Low Pass FIR Filter with and without GA

Fig. 7: Round Off Noise Power Spectrum of Low Pass FIR Filter with and without GA

Fig. 8: Plot of GA Generation verses Best Population

IV. CONCLUSION In this paper, we present the design of low pass FIR filter using stochastic search techniques inspired by the principles of natural selection and natural genetics. GA is based on the genetic processes of biological organisms. GA uses the principle of natural selection and “survival of the fittest�. All the responses like magnitude response, phase response, step response, impulse response, pole zero plot and so on are represented above, using these responses we analyze that we have got better result, the

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Low Pass FIR Filter Design using Genetic Algorithm (IJSTE/ Volume 3 / Issue 06 / 017)

stop band frequency achieved is 0.48 which is very good using filter order only 10. So that, it reduces computational complexity very much. Here the number of population is 40 and number of generation is 300.

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[3] An-Xin ZHAO, Xiao-Jun TANG, Zhong-Hua ZHANG, Jun-Hua LIU, “The Optimal Design Method of FIR Filter Using Improved Genetic Algorithm”, IEEE 9th conference on IndustrialElectronicsandApplication(ICIEA),china,vol.no.40,pp.452-455,2014.

[4] Kamini Upadhyay, Manjeet Kumar, Tarun Kumar rawat,”Optimal Design Of Weighted Least Square Based Fractional Delay FIR Filter Using Genetic Algorithm”, International conference on signal propagation and computer technology (ICSPCT),New Delhi,vol.no.62,pp.53-58,2014.

[5] Sabbir U.Ahmad, Andreas Antoniou, “Cascade-Form Multiplierless FIR Filter Design Using Orthogonal Genetic Algorithm,” IEEE International Symposium on Signal Processingand Information Technology,canada,vol.no. 56, pp.932-937,2006.

[6] Sabah M. Ahmed, “ Design of FIR Filters with Arbitrary Amplitude and Phase Specifications using Genetic Algorithm”, International conference on signal propagation andcomputertechnology (ICSPCT),Egypt,vol.no.37,pp.648-651,2004.

[7] David W. Redmill, David R. Bull, “Design of Low Complexity FIR Filters using Genetic Algorithms and Directed Graphs”, pp.168-173,1997.

[8] G. Wade, A. Roberts, G. Williams, “Multiplierless FIR Filter Design using A Genetic Algorithm”, IEEE Proceedings: Image Signal Processing,vol.no.141,pp.175-180,1994.

[9] Pradeep Kaur, Simarpreet Kaur, “Optimization of FIR Filters Design using Genetic Algorithm”, International Journal of Emerging Trends & Technology in Computer Science (IJETTCS),vol.no.1,pp.228-232,2012.

[10] Alireza Rezaee, “Using Genetic Algorithms for Designing of FIR Digital Filters”, ICTACT Journal on Soft Computing,pp.18-22,2010.

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