18 October 2018

DFT meaning

In the digital communication system, the DFT stands for Discrete Fourier transform, it is a finite duration frequency sequence which is obtained by sampling one period of Fourier transform. Sampling is done at 'N' equally spaced points, over the period extending from o to around range of 2π.

Mathematical equations :

The DFT of discrete sequence sequence is x(n) and  is denoted by X(k). It is given by,

X(K) = ∑    x(n) . e –j2πkn/N

Here k = 0,1,2,3.......N-1

Since this summation is taken for N point, it is called as N point of discrete Fourier transform called DFT.

We can obtain a discrete sequence x(n) from its DFT. It is called an inverse discrete Fourier transform. It is given by, 

X(n) =1/N ∑    x(k) . e –j2πkn/N

Here n = 0,1,2,3.......N-1

This is called as N point IDFT.