This document discusses algorithms for the Fast Fourier Transform (FFT). It describes the Decimation in Time (DIT) and Decimation in Frequency (DIF) categories of FFT algorithms. Specifically, it outlines the Radix-2 DIT-FFT algorithm, which decomposes an N-point sequence into even and odd samples, obtaining the N-point discrete Fourier transform from the discrete Fourier transforms of the two smaller sequences, reducing arithmetic operations. It further explains that in DIT, the sampling interval is decimated by a factor of two at each stage when calculating the N-point discrete Fourier transform starting from two-point transforms.
2. Category 1:
• DIT (decimation in time)
• DIF(decimation in frequency)
• Radix-2 DIT-FFT Algorithm
• This algorithm is based on decomposing an N-point sequence
(assume N =2^l,l = integer) into two N=2-point sequences (one of
even samples and another of odd samples) and obtaining the N-point
DFT in terms of the DFTs of these two sequences. This operation by
itself results in some savings of the arithmetic operations.
3. Cont..
• To obtain the N-point DFT we have to go back starting with two-point
DFTs. At each stage of going back the sampling interval is decimated
by a factor of 2. Hence the name decimation in time (DIT).
