## Introduction to Fourier AnalysisComprehensive, 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 |

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### Contents

Background | 3 |

Fourier Series for Periodic Functions | 9 |

The Fourier Integral | 62 |

Copyright | |

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### Common terms and phrases

Accompanying Disk aliasing analysis equation analytical definition band-limited called canonical-0 Chapter circular convolution complex exponentials computed continuous converge convolution product convolved cosine derivative Dirac delta discontinuities discrete circular convolution discrete Fourier transform electrical network energy estimates EXAMPLE Exercise fast Fourier transform FFT spectrum FFT system find the Fourier finite following sketch Fourier analysis Fourier coefficients Fourier series Fp(n fp(t frequency domain gives gk and hk H(jw impulse response impulse sampling infinite input invert linear convolution Load LTI system magnitude spectrum MAIN MENU mathematical MAX NEGATIVE MAX POSITIVE multiplied node Observe obtained odd function orthogonality output Parseval's theorem periodic function periodic waveform phase spectrum postprocessor PRIMARY PLOT pulse x(t result SAMPLED PULSE FRACTION sampling instants Section sequence shown in Figure signal span restriction spectra successive differentiation synthesis equation Table Theorem 5.1 time-domain values vector verify zero