ABSTRACT

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.

chapter 1|3 pages

Mathematical Formulae

chapter 2|2 pages

Impulse Function Modeling

chapter 3|3 pages

Signal Properties

chapter 4|2 pages

Continuous Time Convolution

chapter 5|9 pages

Discrete Linear and Circular Convolution

chapter 6|18 pages

Eigenfunctions and Orthogonal Polynomials

chapter 8|13 pages

Gram-Schmidt Orthonormalization Procedure

chapter 12|4 pages

Continuous Fourier Transform (CFT) Pairs

chapter 16|2 pages

Properties of Bilateral Laplace Transforms

chapter 17|2 pages

Unilateral Laplace Transform (ULT) Pairs

chapter 18|6 pages

COMPLEX CONVOLUTION (Laplace Transform)

chapter 22|11 pages

Graphical Derivation of DFT from CFT

chapter 23|11 pages

Analytical Derivation of FFT Algorithm

chapter 24|3 pages

Convergence of Bilateral Z-Transforms

chapter 25|2 pages

Properties of Bilateral Z-Transforms

chapter 26|4 pages

Unilateral Z-Transform Pairs

chapter 27|6 pages

COMPLEX CONVOLUTION (Z-Transforms)

chapter 28|3 pages

Truncation Windows

chapter 29|5 pages

Linear Spaces

chapter 30|26 pages

Basic Theory of Matrices

chapter 31|25 pages

Eigenvalues and Eigenvectors of Matrices

chapter 32|11 pages

Singular Value Decomposition (SVD)

chapter 33|12 pages

Vector and Matrix Differentiation

chapter 34|33 pages

State Space Techniques