Linear Systems Properties : A Quick Reference book cover
1st Edition

Linear Systems Properties
A Quick Reference

ISBN 9780429332951
Published February 27, 2021 by CRC Press
304 Pages

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Book Description

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

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