Design of Finite Impulse Response Filter Using Chaotic Differential Evolution Algorithm

Abstract

In this dissertation work, an approach to design a finite impulse response filter having linear phase has been proposed. A digital filter design procedure has to obtain such a set of filter coefficients that expected frequency specification of the signal are met. The proposed approach relies on chaotic differential evolution evolution algorithm (CDE) to generate the filter coefficients. The chaotic differential evolution (CDE) algorithm is a modification of conventional differential evolution (DE) algorithm, which depends on chaotic sequence for its performance improvement. A uniformly distributed random number generation is very important for better performance of stochastic algorithm. Chaotic map is similar to uniform random number generating function with better statistical and dynamic properties. The chaotic sequence provides better balance between the exploration and exploitation capability of the algorithm. The performance of proposed algorithm is analysed by experimentation with generalized benchmark problems. Low pass and high pass FIR filters of 20th and 30th order have been designed using CDE approach. Least square error is used as an objective function to measure the deviation of frequency response of designed filter from the ideal response. The ripple constraint is introduced in order to reduce the magnitude of ripples present in pass band and stop band regions of filter. The ripple constraint is taken care of using penalty method. The simulation results shows that proposed CDE approach with Tent map outperforms conventional DE algorithm in providing maximum stop band attenuation and minimum stop band and pass band ripples in frequency response. The application of CDE approach for filtering the power line interference (PLI) effected electrocardiogram (ECG) signal is also included in this research work. The experimental results have shown that the proposed approach has ability to design a filter as per desired specifications.