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Inverse DFT

The inverse DFT (the IDFT) is given by

$\displaystyle x(t_n) = \frac{1}{N}\sum_{k=0}^{N-1}X(\omega_k )e^{j\omega_k t_n}, \qquad n=0,1,2,\ldots,N-1.
$

The inverse DFT is written using `$ =$ ' instead of ` $ \isdeftext $ ' because the result follows from the definition of the DFT, as we will show in Chapter 6.


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``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 © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA