Algorithm Collections for Digital Signal Processing Applications Using Matlab

Preface. Acknowledgments. Chapter 1 ARTIFICIAL INTELLIGENCE. 1 Particle Swarm Algorithm. 1-1 How are the values for the variables x and y are updated in every Iteration? 1-2 PSO Algorithm to maximize the function F(X, Y, Z). 1-3 m-Program for PSO Algorithm. 1-4 Program Illustration. 2 Genetic Algorithm. 2-1 Roulette Wheel Selection Rule. 2-2 Example. 2-2-1 m-Program for Genetic Algorithm. 2-2-2 Program Illustration. 2-3 Classification of Genetic Operators. 2-3-1 Simple Crossover. 2-3-2 Heuristic Crossover. 2-3-3 Arith crossover. 3 Simulated Annealing. 3-1 Simulated Annealing algorithm. 3-2 Example. 3-3 m-program for simulated Annealing. 4 Back propagation Neural Network. 4-1 Single Neuron architecture. 4-2 Algorithm. 4-3 Example. 4-4 m-program for training the Artificial Neural Network for the problem proposed in the previous section. 5 Fuzzy Logic Systems. 5-1 Union and Intersection of two fuzzy sets. 5-2 Fuzzy logic systems. 5-2-1 Algorithm. 5-3 Why Fuzzy logic systems? 5-4 Example. 5-5 m-program for the realization of fuzzy logic system for the Specifications given in section 5-4. 6 Ant Colony Optimization. 6-1 Algorithm. 6-2 Example. 6-3 m-program for finding the optimal order using Ant colony technique for the specifications given in the section 6-2. Chapter 2 PROBABILITY AND RANDOM PROCESS. 1 Independent Component Analysis. 1-1 ICA for tow mixed signals. 1-1-1 ICA Algorithm. 1-2 m-program for Independent Component Analysis. 2 Gaussian Mixture Model. 2-1 Expectation-Maximization Algorithm. 2-1-1 Expectation stage. 2-1-2 Maximization stage. 2-2 Example. 2-3 m-program for Gaussian Mixture model. 3 K-means Algorithm for Pattern recognition. 3-1 K-means Algorithm. 3-2 Example. 3-3 m-program for the k-means Algorithm applied for the example given in section 3-2. 4 Fuzzy K-means Algorithm for Pattern recognition. 4-1 Fuzzy k-means Algorithm. 4-2 Example. 4-3 m-program for the Fuzzy k-means algorithm applied for the example given in section 4-2. 5 Mean and Variance Normalization. 5-1 Algorithm. 5-2 Example. 5-3 m-program for Mean and Variance Normalization. Chapter 3 NUMERICAL LINEAR ALGEBRA. 1 Hotelling Transformation. 1-1 Diagonalization of the matrix CM. 1-2 Example. 1-3 m-program for Hotelling Transformation. 2 Eigen Basis. 2-1 Example. 3 Singular Value Decomposition. 3-1 Example. 4 Projection Matrix. 4-1 Projection of the vector a on the vector b. 4-2 Projection of the vector on the plane described by the two columns of the matrix X. 4-2-1 Example 1. 4-2-2 Example 2. 5 Orthonormal Vectors. 5-1 Gram-Schmidt Orthogonalization procedure. 5-2 Example. 5-3 Need for orthonormal basis. 5-4 m-program for Gram-Schmidt Orthogonalization procedure. 6 Computation of the powers of the matrix A. 7 Determination of Kth element in the sequence. 8 Computation of Exponential of the matrix A. 9 Solving Differential equation using Eigen decomposition. 10 Computation of Pseudo Inverse of the matrix A. 11 Computation of Transformation matrices. 11-1 Transformation matrix for Fourier transformation. 11-2 Transformation matrix for Basis co-efficient transformation. 11-3 Transformation matrix for obtaining co-efficient of Eigen basis. 11-4 Transformation matrix for obtaining co-efficient of Wavelet Basis. 12 System stability test using Eigen values. 13 Positive definite matrix test for minimal location of the function f(x1, x2, x3, x4...xn) 14 Wavelet transformation using matrix method. 14-1 Haar Transformation. 14-1-1 Example. 14-1-2 m-program for Haar forward and inverse transformation. 14-2 Daubechies-4 Transformation. 14-2-1 Example. 14-2-2 m-program for Daubechies-4 forward and inverse transformation. Chapter 4 SELECTED APPLICATIONS. 1 Ear Pattern