NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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The canonical form of an exponential function, as typically used in signal processing, is
where is called the time constant of the exponential. is the peak amplitude, as before. The time constant is the time it takes to decay by , i.e.,
A normalized exponential decay is depicted in Fig. 5.5.