Title :
What is the fast Fourier transform?
Author :
Cochran, William T. ; Cooley, James W. ; Favin, David L. ; Helms, Howard D. ; Kaenel, Reg A. ; Lang, William W. ; Maling, George C., Jr. ; Nelson, David E. ; Rader, Charles M. ; Welch, Peter D.
Author_Institution :
Bell Telephone Laboratories, Inc., Holmdel, N. J.
Abstract :
The fast Fourier transform is a computational tool which facilitates signal analysis such as power spectrum analysis and filter simulation by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (referred to as a time series). In this paper, the discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method (fast Fourier transform) for computing this transform is derived, and some of the computational aspects of the method are presented. Examples are included to demonstrate the concepts involved.
Keywords :
Analytical models; Computational modeling; Digital filters; Discrete Fourier transforms; Fast Fourier transforms; Fourier transforms; Laboratories; Signal analysis; Telephony; Time series analysis;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/PROC.1967.5957
