1st Edition

Transforms and Applications Primer for Engineers with Examples and MATLAB®

By Alexander D. Poularikas Copyright 2010
    567 Pages 188 B/W Illustrations
    by CRC Press

    567 Pages
    by CRC Press

    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.

    Signals and Systems
    Signals
    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
    Appendix

    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
    Appendix
    Hilbert Transforms
    Definition
    Hilbert Transforms, Properties and the Analytic Signal
    Hilbert Transform Properties and Hilbert Pairs
    Appendices
    Index

    Biography

    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