Sinusoids and Exponentials

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Sinusoids and Exponentials

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Sinusoids and Exponentials

This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, $t_{60}$, in-phase and quadrature sinusoidal components, theanalytic signal, positive and negative frequencies, constructive anddestructive interference, invariance of sinusoidal frequency in linear time-invariant systems, circular motion as the vector sum of in-phase and quadrature sinusoidal motions, sampled sinusoids, generating sampled sinusoids from powers of $z$, and plot examples using Mathematica.



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