Fast Fourier Transform is implemented where fast response is required. F.F.T is fast implementation of D.F.T. In F.F.T then number of computations are reduced as a result it is computationally faster than D.F.T.
In this experiment, we computed the F.F.T of signals having N=4 and N=8.
Radix-2 algorithm is used for computing F.F.T of an input signal i.e the input signal must 2^N points. To achieve this zero padding of the input signal is done. The input and output sequence in radix-2 F.F.T algorithm is in bit reverse manner.
We also calculated the number of computations required to calculate the F.F.T of a given signal and thus verified that F.F.T is computationally faster than D.F.T.
In this experiment, we computed the F.F.T of signals having N=4 and N=8.
Radix-2 algorithm is used for computing F.F.T of an input signal i.e the input signal must 2^N points. To achieve this zero padding of the input signal is done. The input and output sequence in radix-2 F.F.T algorithm is in bit reverse manner.
We also calculated the number of computations required to calculate the F.F.T of a given signal and thus verified that F.F.T is computationally faster than D.F.T.
FFT is faster to implement as it does parallel processing
ReplyDeleteFFT of radix 2 divides the input into two N/2 pt DFT's. Similarly N/2 is divided into two N/4 sequences, decreasing the computations required, making it faster.
ReplyDeleteIt is useful for large data input sequences
ReplyDeleteFFT is faster and the number of complex and real additions and multiplications are also lesser than that of DFT
ReplyDeleteWe can also use radix-3 or radix-5, etc
ReplyDeleteBut radix-2 gives the best results
ReplyDeleteWell written
ReplyDeleteDIFFFT corresponds to decimation in time and DIFFFT corresponds to decimation in frequency
ReplyDeleteSome trivial calculations are avoided by this algoithm and hence it is faster
ReplyDeleteFFT us faster than DFT
ReplyDelete