[...]... made clear using MATLAB programs This book will be useful for the Beginners Research scholars and Students who are doing research work on practical applications of Digital Signal Processing using MATLAB xiii Acknowledgments I am extremely happy to express my thanks to the Director Dr M.Chidambaram, National Institute of Technology Trichy India for his support I would also like to thank Dr B.Venkatramani,... Madras India for their valuable suggestions Last but not least I would like to thank those who directly or indirectly involved in bringing up this book sucessfully Special thanks to my family members father Mr E.Sankara subbu, mother Mrs E.S.Meena, Sisters R.Priyaravi, M.Sathyamathi, E.S.Abinaya and Brother E.S.Anukeerthi Thanks E.S .Gopi xv Chapter 1 ARTIFICIAL INTELLIGENCE Algorithm Collections 1... Genetic Algorithm When you run the algorithm again, it may end up with Global maxima The chromosomes generated randomly during the first generation affects the best solution obtained using genetic algorithm Best chromosome at every generation is collected Best among the collection is treated as the final Best solution which maximizes the function f(x) 2.2.1 M-program for genetic algorithm The Matlab. .. minima As iteration goes on increasing the values selected for the variable ‘x’ is moving towards the global minima which can be noted from the figure 1-8 22 Chapter 1 Figure 1-8 Illustration of Simulated Annealing 2 Figure 1-9 Illustration of Simulated Annealing 3 1 Artificial Intelligence 3.3 23 M-program for Simulated Annealing Matlab program for minimizing the function f(x)= x+10*sin(5*x)+ 7*cos(4*x)+sin(x),where... Matlab program for obtaining the best solution for maximizing the function f(x) = x+10*sin (5*x) +7*cos (4*x) +sin(x) using Genetic Algorithm is given below 12 geneticgv.m clear all, close all pop=0:0.001:9; pos=round(rand(1,10)*9000)+1; pop1=pop(pos); BEST=[]; for iter=1:1:100 col1=[]; col2=[]; for do=1:1:10 r1=round(rand(1)*9)+1; r2=round(rand(1)*9)+1 ; r3=rand; v1=r3*pop1(r1)+(1-r3)*pop1(r2); v2=r3*pop1(r2)+(1-r3)*pop1(r1);...Preface The Algorithms such as SVD, Eigen decomposition, Gaussian Mixture Model, PSO, Ant Colony etc are scattered in different fields There is the need to collect all such algorithms for quick reference Also there is the need to view such algorithms in application point of view This Book attempts to satisfy the above requirement Also the algorithms are made clear using MATLAB programs This... fn(z1)’ the number ‘z2’ is selected for the next generation and so on Figure 1-4 Roulette Wheel 1 Artificial Intelligence 11 The above operation defined as the simulation for rotating the roulette wheel and selecting the sector is repeated ‘L’ times for selecting ‘L’ values for the next generation Note that the number corresponding to the big sector is having more chance for selection The process of generating... generation Algorithm flow is terminated after attaining the maximum number of iterations In this example Maximum number of iterations used is 100 The Best solution for the above problem is obtained in the thirteenth generation using Genetic algorithm as 4.165 and the corresponding fitness function f(x) is computed as 8.443 Note that Genetic algorithm ends up with local maxima as shown in the figure 1-5 This... zero within 35 iterations Figure 1-2 shows the zoomed version to show how the position of x and y are varying until they reach the steady state 1 2 Chapter 1 Figure 1-1 PSO Example zoomed version Figure 1-2 PSO Example 1.1 How are the Values of ‘x and y’ are Updated in Every Iteration? The vector representation for updating the values for x and y is given in Figure 1-3 Let the position of the swarms... the value for updating the value for ‘a’ in tth iteration, then nexta at (t+1)th iteration can be computed using the following formula This is considered as the velocity for updating the position of the swarm in every iteration nexta (t+1) = a (t) + Δ a(t+1) where Δ a(t+1) = c1 * rand * (a’ –a ) + c2 * rand * ( global –a ) + w(t)* Δa(t) ‘w ( t )’ is the weight at tth iteration The value for ‘w’ is . class="bi x0 y0 w0 h0" alt="" Algorithm Collections for Digital Signal Processing Applications Using Matlab Algorithm Collections for Digital Signal Processing Applications Using Matlab E. S. Gopi National. Algorithms such as SVD, Eigen decomposition, Gaussian Mixture Model, PSO, Ant Colony etc. are scattered in different fields. There is the need to collect all such algorithms for quick reference. Also. inverse transformation 125 1 4-2 Daubechies-4 Transformation 127 1 4-2 -1 Example 128 1 4-2 -2 M-file for daubechies 4 forward and inverse transformation 131 Chapter 4 SELECTED APPLICATIONS 135