Introduction to Fourier Analysis

Contains 36 lectures solely on Fourier analysis and the FFT. Time and frequency domains, representation of waveforms in terms of complex exponentials and sinusoids, convolution, impulse response and the frequency transfer function, modulation and demodulation are among the topics covered. The text is linked to a complete FFT system on the accompanying disk where almost all of the exercises can be either carried out or verified. End-of-chapter exercises have been carefully constructed to serve as a development and consolidation of concepts discussed in the text. CONTINUOUS FOURIER ANALYSIS.

Background.

Fourier Series for Periodic Functions.

The Fourier Integral.

Fourier Transforms of Some Important Functions.

The Method of Successive Differentiation.

Frequency-Domain Analysis.

Time-Domain Analysis.

The Properties.

The Sampling Theorems.

DISCRETE FOURIER ANALYSIS.

The Discrete Fourier Transform.

Inside the Fast Fourier Transform.

The Discrete Fourier Transform as an Estimator.

The Errors in Fast Fourier Transform Estimation.

The Four Kinds of Convolution.

Emulating Dirac Deltas and Differentiation on the Fast Fourier Transform.

THE USER'S MANUAL FOR THE ACCOMPANYING DISKS.

Appendices.

Answers to the Exercises.

Index. NORMAN MORRISON, PhD, is an instructor in the Electrical and Electronics Engineering Department at the University of Cape Town in South Africa. Comprehensive, user friendly, and pedagoicaly structured ... a fast, easy way to learn, about the electrical engineer's most important mathematical tool Based on a groundbreaking one-semester course originated by Professor Norman Morrison at the University of Cape Town, this book serves equally well as a course text and a self-study guide for professionals. Offering only relevant mathematics, it covers all the core principles of electrical engineering contained in Fourier analysis, including the time and frequency domains; the representation of waveforms in terms of complex exponentials and sinusoids; complex exponentials and sinusoids as the eigenfunctions of linear systems; convolution; impulse response and the frequency transfer function; magnitude and phase spectra; and modulation and demodulation.
* Covers Fourier analysis exclusively for electrical engineering students and professionals
* Offers a complete FFT system contained on the enclosed disks (one for IBM compatibles, the other for Macintosh)
* Includes dozens of examples drawn from electrical engineering
* Packed with exercises, samples, and end-of-chapter problem sets