December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and Systems
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11.5 DISCRETE FOURIER TRANSFORM
We know that the Fourier transform of discrete sequence x(n) is given by
where X(ω) is the continuous function of ω and the range of ω is from −π to +π or 0 to 2π. Since X(ω) is the continuous function of ω, it is not possible to calculate it on a digital computer or a digital signal processor. Hence it is necessary to calculate it only for discrete values of ω. When Fourier transform is calculated at discrete points, it is called discrete Fourier transform (DFT) which is denoted by X(k) and is expressed as
In Eq. (11.19) X(k) is called DFT which is computed at k = 0, 1, 2, ……., N −1 i.e., N discrete ...
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