NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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
<< Previous page TOC INDEX Next page >>
Positive Integer Exponents
The ''original'' definition of exponents which ''actually makes sense'' applies only to positive integer exponents:
where is real.
Generalizing this definition involves first noting its abstract mathematical properties, and then making sure these properties are preserved in the generalization.