Transforms and Applications Primer for Engineers with Examples and MATLAB®: 1st Edition (Paperback) book cover

Transforms and Applications Primer for Engineers with Examples and MATLAB®

1st Edition

By Alexander D. Poularikas

CRC Press

567 pages | 188 B/W Illus.

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Paperback: 9781420089318
pub: 2010-03-11
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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.


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

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



About the Author

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.

About the Series

Electrical Engineering Primer Series

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BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Mobile & Wireless Communications