1st Edition

# Linear Systems Properties A Quick Reference

304 Pages
by CRC Press

304 Pages
by CRC Press

Also available as eBook on:

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.
• 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
References
Index

### Biography

Dr. Venkatarama Krishnan received his Ph.D. in Electrical Engineering from the University of Pennsylvania, he has 41 years of teaching experience inclduing faculty positions at the University of Massachusetts, Indian Institute of Science, Polytechnic Institute of Brooklyn, University of Pennsylvania, Villanova University and Princeton University. He has extent experience in research and his hobbies include graphic arts, photography, Shakespeare, painting, music, and travelling.