next Mathematics of the DFT
previous DFT Definition
up Introduction to the DFT   Contents   Global Contents
global_index Global Index   Index   Search


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 `$ =$' instead of `$ \isdef $' because the result follows from the definition of the DFT, as we will show in Chapter 6.


next Mathematics of the DFT
previous DFT Definition
up Introduction to the DFT   Contents   Global Contents
global_index Global Index   Index   Search

``Mathematics of the Discrete Fourier Transform (DFT)'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.

(Browser settings for best viewing results)
(How to cite this work)
(Order a printed hardcopy)

Copyright © 2003-10-09 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  (automatic links disclaimer)