Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

The Fast Fourier Transform for Experimentalists Part II: Convolutions



D Donnelly, Bert W. Rust


The discrete Fourier transform (DFT) is a widely used tool for the analysis of measured time series data. The Cooley-Tukey fast Fourier transform (FFT) algorithm gives an extremely fast and efficient implementation of the DFT. This is the first of a series of three articles which will describe the use of the FFT for experimental practitioners. This installment gives fundamental definitions and tells how to use the FFT to estimate power and amplitude spectra of a measured time series. It discusses the use of zero padding, the problem of aliasing, the relationship of the inverse DFT to Fourier series expansions, and the use of tapering windows to reduce the sidelobes on the peaks in an estimated spectrum.
Computing in Science & Engineering


autocorrelation function, convolutions, correlogram, Fourier transform, periodogram


Donnelly, D. and Rust, B. (2005), The Fast Fourier Transform for Experimentalists Part II: Convolutions, Computing in Science & Engineering, [online], (Accessed June 21, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created July 31, 2005, Updated October 12, 2021