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Mathematical summary for digital signal processing applications with Matlab, 2010

Langue : Anglais

Auteur :

Couverture de l’ouvrage Mathematical summary for digital signal processing applications with Matlab
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-Mathematical readers and is very much suitable for the beginners who are doing research in Digital Signal Processing.
1. Matrices. 1-1 Properties of vectors. 1-2 Properties of Matrices. 1-3 LDU Decomposition of the arbitrary matrix. 1-4 PLDU Decomposition of the arbitrary matrix. 1-5 Vector space and its properties. 1-6 Linear independence, Span, Basis and the Dimension of the Vector Space. 1-7 Four Fundamental Vector spaces of the Matrix. 1-8 Basis of the Four Fundamental Vector spaces of the Matrix. 1-9 Observations on the Results of the Example 1-12. 1-10 Vector Representation with different basis. 3-11 Linear transformation of the vector. 1-12 Transformation matrix with different basis (Similar Matrices). 3-13 Orthogonality. 1-14 System of Linear Equation. 1-15 Solutions for the system of Linear Equation [A] x = b. 1-16 Gram-Schmidt Orthogonalization procedure for obtaining orthonormal basis. 1-17 QR Factorization. 1-18 Eigen values and the Eigen Vectors. 1-19 Geometric Multiplicity (vs) Algebraic Multiplicity. 1-20 Diagonalization of the matrix. 1-21 Schurs Lemma. 1-22 Hermitian Matrices. 1-23 Unitary Matrices. 3-24 Normal Matrices. 1-25 Applications of Diagonalization of the non-deficient matrix. 1-26 Singular Value Decomposition(SVD). 1-27 Applications of Singular Value Decomposition.
From the reviews:'Summarizes the mathematical background required for the study of digital signal processing. ... The material is presented in a concise outline format, with relatively brief explanations illustrated by simple numerical examples. ... This volume may be useful to advanced students in electrical engineering and other areas of science and engineering who need to review these mathematical subjects before studying digital signal processing. Summing Up: Recommended. Upper-division undergraduates and graduate students.' (B. Borchers, Choice, Vol. 48 (5), January, 2011)

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Ouvrage de 250 p.

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