Negative Exponents

01 Mar 1998

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Negative Exponents

What should $a^{-1}$ be? Multiplying it by gives

Solving $$a^{-1} \$ for $a^{-1}$ then gives

Similarly, we obtain

for all integer values of , i.e., $$\$ .
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GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Negative Exponents

Negative Exponents