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E-book
Author Gopi, E. S.

Title Mathematical summary for digital signal processing applications with Matlab / by E.S. Gopi
Published Dordrecht ; London : Springer, 2010
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Description 1 online resource
Contents Mathematical Summaryfor Digital Signal ProcessingApplications with Matlab; 1 Matrices; 1.1 Properties of Vectors; 1.2 Properties of Matrices; 1.3 LDU Decomposition of the Matrix; 1.4 PLDU Decomposition of an Arbitrary Matrix; 1.5 Vector Space and Its Properties; 1.6 Linear Independence, Span, Basis and the Dimension of the Vector Space; 1.6.1 Linear Independence; 1.6.2 Span; 1.6.3 Basis; 1.6.4 Dimension; 1.7 Four Fundamental Vector Spaces of the Matrix; 1.7.1 Column Space; 1.7.2 Null Space; 1.7.3 Row Space; 1.7.4 Left Null Space; 1.8 Basis of the Four Fundamental Vector Spaces of the Matrix
1.8.1 Column Space1.9 Observations on Results of the Example 1.12; 1.9.1 Column Space; 1.9.2 Null Space; 1.9.3 Left Column Space (Row Space); 1.9.4 Left Null Space; 1.9.5 Observation; 1.10 Vector Representation with Different Basis; 1.11 Linear Transformation of the Vector; 1.11.1 Trick to Compute the Transformation Matrix; 1.12 Transformation Matrix with Different Basis; 1.13 Orthogonality; 1.13.1 Basic Definitions and Results; 1.13.2 Orthogonal Complement; 1.14 System of Linear Equation; 1.15 Solutions for the System of Linear Equation [A] x=b; 1.15.1 Trick to Obtain the Solution
1.16 Gram Schmidt Orthonormalization Procedure for Obtaining Orthonormal Basis1.17 QR Factorization; 1.18 Eigen Values and Eigen Vectors; 1.19 Geometric Multiplicity (Versus) Algebraic Multiplicity; 1.20 Diagonalization of the Matrix; 1.21 Schur's Lemma; 1.22 Hermitian Matrices and Skew Hermitian Matrices; 1.23 Unitary Matrices; 1.24 Normal Matrices; 1.25 Applications of Diagonalization of the Non-deficient Matrix; 1.26 Singular Value Decomposition; 1.27 Applications of Singular Value Decomposition; 2 Probability; 2.1 Introduction; 2.2 Axioms of Probability; 2.3 Class of Events or Field (F)
2.4 Probability Space (S, F, P)2.5 Probability Measure; 2.6 Conditional Probability; 2.7 Total Probability Theorem; 2.8 Bayes Theorem; 2.9 Independence; 2.10 Multiple Experiments (Combined Experiments); 2.11 Random Variable; 2.12 Cumulative Distribution Function (cdf) of the Random Variable x̀'; 2.13 Continuous Random Variable; 2.14 Discrete Random Variable; 2.15 Probability Mass Function; 2.16 Probability Density Function; 2.17 Two Random Variables; 2.18 Conditional Distributions and Densities; 2.19 Independent Random Variables; 2.20 Some Important Results on Conditional Density Function
2.21 Transformation of Random Variables of the Type Y=g(X)2.22 Transformation of Random Variables of the Type Y1 = g1(X1,X2), Y2 = g2(X1, X2); 2.23 Expectations; 2.24 Indicator; 2.25 Moment Generating Function; 2.26 Characteristic Function; 2.27 Multiple Random Variable (Random Vectors); 2.28 Gaussian Random Vector with Mean Vector X and Covariance Matrix CX; 2.29 Complex Random Variables; 2.30 Sequence of the Number and Its Convergence; 2.31 Sequence of Functions and Its Convergence; 2.32 Sequence of Random Variable; 2.33 Example for the Sequence of Random Variable
Summary Mathematical summary for Digital Signal Processing Applications with Matlab consists of Mathematics which is not usually dealt in the DSP core subject, but used in DSP applications. Matlab programs with illustrations are given for the selective topics such as generation of Multivariate Gaussian distributed sample outcomes, Bacterial foraging algorithm, Newton's iteration, Steepest descent algorithm, etc. are given exclusively in the separate chapter. Also Mathematical summary for Digital Signal Processing Applications with Matlab is written in such a way that it is suitable for Non-Mathematica
Bibliography Includes bibliographical references and index
Notes Print version record
Subject MATLAB.
Signal processing -- Digital techniques -- Mathematics.
Form Electronic book
LC no. 2009944069
ISBN 9048137470
9789048137473
(hbk.)
(hbk.)