Open Access Open Access  Restricted Access Subscription or Fee Access

A Genetic Algorithm for Optimization of MSE & Ripples in Linear Phase Low Pass FIR Filter & Also Compare with Cosine Window Techniques

Vandana Vikas Thakare, Rahul Kumar Sahu

Abstract


Cosine Window Techniques such as Hamming, Hanning etc. are used to simply design the Finite Impulse Response (FIR) digital Filters. Window function is a scientific function which works on Mathematics by calculating the impulse response of best digital filters. Windowing function is mainly conciliation between the reduction of ripples and Mean Square Error (MSE). But in the proposed research work; Genetic Algorithm (GA) reduces more MSE as well as ripples as compare to Hamming & Hanning window. Bouncing of ripples is known as Gibbs Phenomenon. GA is a Computational search Algorithm which is basically works on the natural selection of genes, chromosomes, crossover and mutation. The proposed paper contains the optimized coefficients, magnitude response, phase response, pole zero map & impulse response of symmetric linear phase low pass FIR Filter.
Index Terms– FIR filter, Mean Square Error (MSE), Hamming, Hanning window, Genetic Algorithm (GA)

Full Text:

PDF

References


Sanjit K. Mitra, Digital Signal Processing: A Computer-based Approach, 2nd edition, Chap. [3], 217-289, (2001)

A. Antoniou, Digital Filters: Analysis, Design and Applications, 2nd Ed. Mc.Graw Hill, 1993

Proakis, John G., and Dimitris G. Manolakis, (1996), “Digital Signal Processing: Principles, Algorithms, and Applications”, 3rd Edition, Prentice-Hall, Inc.

S. Salivahnan, A. Vallaraj, C. Gnanapriya, “Digital Signal Processing”, 19th reprint Edition, 2006, Tata McGraw-Hill.

http://researchgate.net/why_windows_are_used, (2015)

D.E. Goldberg, Genetic Algorithm, In Search, Optimization and Machine Learning, Addison Wesley, Reading, MA, (1989)

S.Rajasekaran, and G.A. Vijayalakshmi Pai, “Neural Networks, Fuzzy Logic, and Genetic Algorithms: Synthesis and Applications”, 17th Edition, Eastern Economy Edition Chap [8], 225-252, (2014)

Sivanandam, S.N., and S.N. Deepa, “Introduction to Genetic Algorithms” Springer, Chap. [2-8], (2008)

Theodore W. Manikas and James T. Cain. Genetic Algorithms vs. Simulated Annealing: A Comparison of Approaches for Solving the Circuit Partitioning Problem. University of Pittsburgh, Dept. of Electrical Engineering, May (2010)

Wade, G., A. Roberts and G. Williams, (1994), “Multiplier-less FIR filter design using a genetic algorithm”. IEE Proc.-Vis (Image Signal Process.), Vol. 141, No. 3, pp.175-180

Haupt, Randy L., and Sue Ellen Haupt, (2004), “PRACTICAL GENETIC ALGORITHMS”, 2nd EDITION, John Wiley & Sons Inc.

K. S. Tang, K. F. Man, S. Kwong and Q. HE, (1996), “Genetic Algorithms and their Applications”, IEEE SIGNAL PROCESSING, Vol. (), No. (), p. 22– 37

Global Optimization Toolbox, User’s Guide, version R2014b, www.mathworks.com, Chap. [2-5], (2014)

Filter Design Toolbox, For use with MATLAB, User’s Guide version 2, www.mathworks.com, Chap. [1-4], 2013

Roy, T.K; Morshed,M. “Performance analysis of low pass FIR filters design using Kaiser, Gaussaian and Turkey window function”, Advances in Electrical Engineering (2013), IEEE conference pp. 1-6

Karaboga, Nurhan and Bahadir Cetinkaya, “Optimal design of minimum phase digital FIR filters by using Genetic Algorithm”, IEEE. PP. 24-28. (2013)

D. Suckley, “Genetic Algorithm in the Design of FIR Filters”, IEEE proceeding Circuits, Devices and Systems, Vol. 138, pp. 234-238, Apr 1991.




DOI: https://doi.org/10.37628/jdcas.v1i1.42

Refbacks

  • There are currently no refbacks.