Question

(TCO 7) What is the difference between discrete Fourier transform (DFT) and fast Fourier transform (FFT)? can you please type it cant see images.

Answer 1

The main differences between DFT and FFT are given below:

1. DFT converts equally spaced samples of a function to equivalent sequence of same length of DTFT. FFT makes use of special algorithm to sample a signal over a particular time period or space by dividing into frequency components.  
2. As the interval at which the sampling is done is the reciprocal of the duration of the input sequence, hence DFT is known as the frequency domain representation of the original input sequence as it decomposes a sequence into different frequency components. Hence the sampling can be done in any arbitary frequency component of the spectrum. In FFT, the sampling has to be regular .i.e, frquency components can be calculated only at certain frequencies (Fs/N).
3. FFT is faster than DFT as it factorizes the DFT matrix into the product ofsparse factors. The complexeity of FFT (O(nlogn)) is greatly reduced as compared to DFT (O(n²)).
4. FFT requires much less processing power for the same number of harmonics as in the DFT.