Fast Fourier Transform
An FFT produces exactly the same result as evaluating the DFT directly. The most important difference is that an FFT is much faster. A radix-2 decimation-in-time (DIT) FFT operates by decomposing an N point time domain signal into two N/2 point signal. This is repeated till we get 2 point time domain signals. In DITFFT the output sequence index is in order and the input sequence index is in bit reversed order of the output. In case of DIFFFT, it is the other way round. The number of calculations are reduced in FFT.
Originally posted at: https://chaitanya33.wordpress.com/2017/03/13/fast-fourier-transform/
Originally posted at: https://chaitanya33.wordpress.com/2017/03/13/fast-fourier-transform/
the most commonly used FFT is the Cooley–Tukey algorithm.
ReplyDeletewhy cooley-tuckey algorithm is widely used
DeleteBecause it is radix 2
Deleteother radices can also be used (usually numbers less than 10)
ReplyDeleteYes but radix 2 is best as no. of calculations reduce
DeleteFFT 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.
ReplyDeleteYes
DeleteFFT uses parallel processing so it is difficult to implement
ReplyDeleteParallelizing the simple FFT algorithms will be beneficial to control code complexity and minimize execution time of the process. Hence parallel FFT algorithms are desirable.
Deletedecomposition reduces calculations hence FFT is Fast
ReplyDeleteYes
DeleteFFT is used in filtering algorithms
ReplyDeleteYes it is
DeleteSpectrum improves as no. of sample points increases
ReplyDeleteYes approximation error reduces
DeleteFFT is faster than DFT
ReplyDelete