Algorithm Collections for Digital Signal Processing Applications using Matlab: Algorithm Collections for Digital Signal Processing Applications using Matlab - .pdf

Contents
Preface xiii
Acknowledgments x
Chapter 1 ARTIFICIAL INTELLIGENCE
1 Particle Swarm Algorithm 1
1-1 How are the Values of ‘x’ and ‘y’ are Updated
in Every Iteration? 2
1-2 PSO Algorithm to Maximize the Function F(X, Y, Z) 4
1-3 M-program for PSO Algorithm 6
1-4 Program Illustration 8
2 Genetic Algorithm 9
2-1 Roulette Wheel Selection Rule 10
2-2 Example 11
2-2-1 M-program for genetic algorithm 11
2-2-2 Program illustration 13
2-3 Classification of Genetic Operators 15
2-3-1 Simple crossover 16
2-3-2 Heuristic crossover 16
2-3-3 Arith crossover 17
3 Simulated Annealing 18
3-1 Simulated Annealing Algorithm 19
3-2 Example 19
3-3 M-program for Simulated Annealing 23
v
vii
4 Back Propagation Neural Network 24
4-1 Single Neuron Architecture 25
4-2 Algorithm 27
4-3 Example 29
4-4 M-program for Training the Artificial Neural Network
for the Problem Proposed in the Previous Section 31
5 Fuzzy Logic Systems 32
5-1 Union and Intersection of Two Fuzzy Sets 32
5-2 Fuzzy Logic Systems 33
5-2-1 Algorithm 35
5-3 Why Fuzzy Logic Systems? 38
5-4 Example 39
5-5 M-program for the Realization of Fuzzy Logic System
for the Specifications given in Section 5-4 41
6 Ant Colony Optimization 44
6-1 Algorithm 44
6-2 Example 48
6-3 M-program for Finding the Optimal Order using Ant Colony
Technique for the Specifications given in the Section 6-2
50
Chapter 2 PROBABILITY AND RANDOM PROCESS
1 Independent Component Analysis 53
1-1 ICA for Two Mixed Signals 53
1-1-1 ICA algorithm 62
1-2 M-file for Independent Component Analysis 65
2 Gaussian Mixture Model 68
2-1 Expectation-maximization Algorithm 70
2-1-1 Expectation stage 71
2-1-2 Maximization stage 71
2-2 Example 72
2-3 Matlab Program 73
2-4 Program Illustration 76
3 K-Means Algorithm for Pattern Recognition 77
3-1 K-means Algorithm 77
3-2 Example 77
3-3 Matlab Program for the K-means Algorithm Applied
for the Example given in Section 3-2 78
4 Fuzzy K-Means Algorithm for Pattern Recognition 79
4-1 Fuzzy K-means Algorithm 80
4-2 Example 81
4-3 Matlab Program for the Fuzzy k-means Algorithm Applied
for the Example given in Section 4-2 83
viii Contents
5 Mean and Variance Normalization 84
5-1 Algorithm 84
5-2 Example 1 85
5-3 M-program for Mean and Variance Normalization 86
Chapter 3 NUMERICAL LINEAR ALGEBRA 87
1 Hotelling Transformation 87
1-1 Diagonalization of the Matrix ‘CM’ 88
1-2 Example 88
1-3 Matlab Program 90
2 Eigen Basis 91
2-1 Example 1 91
3 Singular Value Decomposition (SVD) 93
3-1 Example 94
4 Projection Matrix 95
4-1 Projection of the Vector ‘a’ on the Vector ‘b’ 95
4-2 Projection of the Vector on the Plane Described
by Two Columns Vectors of the Matrix ‘X’ 96
4-2-1 Example 97
4-2-2 Example 2 98
5 Orthonormal Vectors 100
5-1 Gram-Schmidt Orthogonalization procedure 100
5-2 Example 101
5-3 Need for Orthonormal Basis 101
5-4 M-file for Gram-Schmidt Orthogonalization Procedure 103
6 Computation of the Powers of the Matrix ‘A’ 103
7 Determination of Kth Element in the Sequence 104
8 Computation of Exponential of the Matrix ‘A’ 107
8.1 Example 107
9 Solving Differential Equation Using Eigen decomposition 108
10 Computation of Pseudo Inverse of the Matrix 109
11 Computation of Transformation Matrices 111
11-1 Computation of Transformation Matrix for the Fourier
Transformation
113
11-2 Basis Co-efficient transformation 115
11-3 Transformation Matrix for Obtaining Co-efficient
of Eigen Basis 117
11-4 Transformation Matrix for Obtaining Co-efficient
of Wavelet Basis 117
12 System Stability Test Using Eigen Values 118
13 Positive Definite Matrix test for Minimal Location
of the Function f (x1, x2, x3, x4…xn) 119
Contents ix
x
14 Wavelet Transformation Using Matrix Method 119
14-1 Haar Transformation 120
14-1-1 Example 122
14-1-2 M-file for haar forward and inverse
transformation 125
14-2 Daubechies-4 Transformation 127
14-2-1 Example 128
14-2-2 M-file for daubechies 4 forward
and inverse transformation 131
Chapter 4 SELECTED APPLICATIONS 135
1 Ear Pattern Recognition Using Eigen Ear 135
1-1 Algorithm 135
1-2 M-program for Ear Pattern Recognition 138
2 Ear Image Data Compression using Eigen Basis 141
2-1 Approach 141
2-2 M-program for Ear Image Data Compression 143
3 Adaptive Noise Filtering using Back Propagation
Neural Network 145
3-1 Approach 146
3-2 M-file for Noise Filtering Using ANN 147
3-3 Program Illustration 149
4 Binary Image Rotation Using Transformation Matrix 150
4-1 Algorithm 151
4-2 M-program for Binary Image Rotation with 45 Degree
Anticlockwise Direction 152
5 Clustering Texture Images Using K-means Algorithm 152
5-1 Approach 153
5-2 M-program for Texture Images Clustering 155
6 Search Engine Using Interactive Genetic Algorithm 156
6-1 Procedure 156
6-2 Example 158
6-3 M-program for Interactive Genetic Algorithm 160
6-4 Program Illustration 165
7 Speech Signal Separation and Denoising Using Independent
Component Analysis 166
7-1 Experiment 1 166
7-2 Experiment 2 167
7-3 M-program for Denoising 169
Contents
1-3 Program Illus tration 140
xi
8 Detecting Photorealistic Images using ICA Basis 170
8-1 Approach 171
8-1-1 To classify the new image into one among the
photographic or photorealistic image 171
8-2 M-program for Detecting Photo Realistic Images
Using ICA basis 172
8-3 Program Illustration 174
9 Binary Image Watermarking Using Wavelet Domain
of the Audio Signal
9-1 Example 175
9-2 M-file for Binary Image Watermarking
in Wavelet Domain of the Audio Signal
176
9-3 Program Illustration 180
Appendix 183
Index 189

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