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Advantages of FFT over DFT

 

FFT computation is less complex as compared to the DFT algorithm.

 

DFT Transform 

 











FFT Transform

 













 
 
Fig: FFT Transform of 8 Point DFT
 
 
In the above figure, it is shown that the basic idea of a fast Fourier transform is to break up a transform of length N into two transforms of length N/2.

To compute the DFT of an N-point sequence it take O(N2) multiplies and adds. The FFT algorithm computes the DFT using O(N log N) multiplies and adds.

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N2 to 2Nlog2N.

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