Linear Systems Properties: A Quick Reference, 1st Edition (Paperback) book cover

Linear Systems Properties

A Quick Reference, 1st Edition

By Venkatarama Krishnan

CRC Press

304 pages

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Paperback: 9780849322914
pub: 1998-03-06

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This pocket book serves as an immediate reference for the various formulae encountered in linear systems, control systems, probability, communication engineering, signal processing, quantum mechanics, and electromagnetic field theory. It includes novel results on complex convolutions; clearly explains real and complex matrix differentiation methods; provides an unusual amount of orthogonal functions; and presents properties of Fourier series, Fourier transforms, Hilbert transforms, Laplace transforms, and z-transforms. Singular value decomposition techniques for matrix inversion are also clearly presented.

This new edition adds material from:

  • Orthogonal functions

  • Linear algebra

  • Matrix analysis

  • Matrix and vector differentiation

  • Singular value decomposition

  • State space techniques

    Other discussions include:

  • Discrete linear and circular convolution

  • Gram-Schmidt orthogonalization procedure

  • Graphical derivation of DFT from CFT

  • Truncation windows

  • Eigenvalues and eigenvectors of matrices

    This succint resource will be particularly useful as a supplement to regular texts, designed for the master's or doctoral student as well as the advanced undergraduate.

  • Table of Contents

    Mathematical Formulae

    Impulse Function Modeling

    Signal Properties

    Continuous Time Convolution

    Discrete Linear and Circular Convolution

    Eigenfunctions and Orthogonal Polynomials

    Useful Orthogonal Polynomials

    Gram-Schmidt Orthogonalization Procedure

    Properties of Continuous Fourier Series

    Fourier Transform from Fourier Series

    Properties of Continuous Fourier Transforms

    Continuous Fourier Transform Pairs

    Inverse Fourier Transforms (Contour Integration)

    Derivation of Hilbert Transforms

    Convergence of Bilateral Laplace Transforms

    Properties of Bilateral Laplace Transforms

    Unilateral Laplace Transform Pairs

    Complex Convolution (Laplace Transforms)

    Properties of Discrete-Time Fourier Series

    Properties of Discrete-Time Fourier Transforms

    **Properties of Discrete Fourier Transforms

    Graphical Derivation of DFT from CFT

    Analytical Derivation of FFT Algorithm

    Convergence of Bilateral z-Transforms

    Properties of Bilateral z-Transforms

    Unilateral z-Transform Pairs

    Complex Convolution (z-Transforms)

    Truncation Windows

    Linear Spaces

    Basic Theory of Matrices

    Eigenvalues and Eigenvectors of Matrices

    Singular Value Decomposition (SVD)

    Vector and Matrix Differentiation

    State Space Techniques



    About the Originator

    About the Series

    Control Series

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    Subject Categories

    BISAC Subject Codes/Headings:
    MATHEMATICS / Differential Equations
    TECHNOLOGY & ENGINEERING / Engineering (General)