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 2*π*. 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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