Title :
The finite Fourier transform
Author :
Cooley, J.W. ; Lewis, E. A W ; Welch, P.D.
Author_Institution :
IBM Watston Research Center, Yorktown Heights, N.Y.
fDate :
6/1/1969 12:00:00 AM
Abstract :
The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.
Keywords :
Books; Convolution; Data analysis; Fast Fourier transforms; Fourier series; Fourier transforms; Frequency; Mathematical analysis; Mathematics; Sampling methods;
Journal_Title :
Audio and Electroacoustics, IEEE Transactions on
DOI :
10.1109/TAU.1969.1162036
