Page 8 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

Contents ix

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
th
7 Determination of K 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 113
Transformation
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