Transforms and Applications Primer for Engineers with Examples and MATLAB®  book cover
1st Edition

Transforms and Applications Primer for Engineers with Examples and MATLAB®

ISBN 9781420089318
Published March 11, 2010 by CRC Press
567 Pages 188 B/W Illustrations

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Book Description

Transforms and Applications Primer for Engineers with Examples and MATLAB® is required reading for engineering and science students, professionals, and anyone working on problems involving transforms. This invaluable primer contains the most essential integral transforms that both practicing engineers and students need to understand. It provides a large number of examples to explain the use of transforms in different areas, including circuit analysis, differential equations, signals and systems, and mechanical vibrations.

Includes an appendix with suggestions and explanations to help you optimize your use of MATLAB

Laplace and Fourier transforms are by far the most widely used and most useful of all integral transforms, so they are given a more extensive treatment in this book, compared to other texts that include them. Offering numerous MATLAB functions created by the author, this comprehensive book contains several appendices to complement the main subjects. Perhaps the most important feature is the extensive tables of transforms, which are provided to supplement the learning process. This book presents advanced material in a format that makes it easier to understand, further enhancing its immense value as a teaching tool for engineers and research scientists in academia and industry, as well as students in science and engineering.

Table of Contents

Signals and Systems
Circuit Elements and Equation
Linear Mechanical and Rotational Mechanical Elements
Discrete Equations and Systems
Digital Simulation of Analog Systems
Convolution of Analog Signals
Convolution of Discrete Signals
Fourier Series
Fourier Series in a Complex Exponential Form
Fourier Series in Trigonometric Form
Waveform Symmetries
Some Additional Features of Periodic Continuous Functions
Fourier Transforms
Other Forms of Fourier Transform
Fourier Transform Examples
Fourier Transform Properties
Examples on Fourier Properties
FT Examples of Singular Functions
Duration of a Signal and the Uncertainty Principle
Applications to Linear-Time Invariant Systems
Applications to Communication Signals
Signals, Noise, and Correlation
Average Power Spectra, Random Signals, Input–Output Relations
FT in Probability Theory
Relatives to the Fourier Transform
Infinite Fourier Sine Transform
Infinite Fourier Cosine Transform
Applications to Boundary-Value Problems
Finite Sine Fourier Transform and Finite Cosine Fourier Transform
Two-Dimensional Fourier Transform
Sampling of Continuous Signals
Fundamentals of Sampling
The Sampling Theorem
Discrete-Time Transforms
Discrete-Time Fourier Transform
Summary of DTFT Properties
DTFT of Finite Time Sequences
Frequency Response of LTI Discrete Systems
Discrete Fourier Transform
Summary of DFT Properties
Multirate Digital Signal Processing and Spectra

Proofs of DTFT Properties
Proofs of DFT Properties
Fast Fourier Transform
Decimation in Time Procedure

Laplace Transform
One-Sided Laplace Transform
Summary of the Laplace Transform Properties
Systems Analysis: Transfer Functions of LTI Systems
Inverse Laplace Transform
Problem Solving with Laplace Transform
Frequency Response of LTI Systems
Pole Location and the Stability of LTI Systems
Feedback for Linear Systems
Bode Plots
Inversion Integral
Complex Integration and the Bilateral Laplace Transform
State Space and State Equations
The z-Transform
The z-Transform
Convergence of the z-Transform
Properties of the z-Transform
z-Transform Pairs
Inverse z-Transform
Transfer Function
Frequency Response of First-Order Discrete Systems
Frequency Response of Higher Order Digital Systems
z-Transform Solution of First-Order Difference Equations
Higher Order Difference Equations
LTI Discrete-Time Dynamical Systems
z-Transform and Random Processes
Relationship between the Laplace and z-Transforms
Relationship to the Fourier Transform
Hilbert Transforms
Hilbert Transforms, Properties and the Analytic Signal
Hilbert Transform Properties and Hilbert Pairs

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Alexander D. Poularikas received his Ph.D. from the University of Arkansas, Fayetteville, and became a professor at the University of Rhode Island, Kingston. He became the chairman of the engineering department at the University of Denver, Colorado, and then became the chairman of the electrical and computer engineering department at the University of Alabama in Huntsville. Dr. Poularikas has authored seven books and has edited two. He has served as the editor-in-chief of the Signal Processing series (1993–1997) with Artech House, and is now the edito- in-chief of the Electrical Engineering and Applied Signal Processing series as well as the Engineering and Science Primer series (1998 to present) with Taylor & Francis. He was a Fulbright scholar, is a lifelong senior member of the IEEE, and is a member of Tau Beta Pi, Sigma Nu, and Sigma Pi. In 1990 and in 1996, he received the Outstanding Educators Award of the IEEE, Huntsville Section. He is now a professor emeritus at the University of Alabama in Huntsville.


This book is a thorough presentation of integral transforms, geared to practicing engineers. MATLAB and MATLAB code are included throughout. … The book’s numerous examples, figures, and tables improve readability, comprehension, and usability of the material presented. Summing Up: Recommended.
CHOICE, January 2011