|You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.|
|Table of Contents Bivariate Data Time Series Fourier Transformation|
|See also: time and frequency, Fourier series, FFT|
The Fourier transformation provides the means to convert a signal from its representation in the time (as it is most often measured) to its representation in the frequency domain. The Fourier transform is reversible, making it possible to choose any representation for processing a signal. The Fourier transform is a generalization of the Fourier series to an infinite interval:
Replacing the integral with a sum leads to the discrete Fourier transform (DFT), which can be applied to digitized data:
For practical situations the Fourier transform in its original form
involves one major problem: it takes too many computational steps to be
performed in real-time for many signals. Fortunately there is a family
of equivalent algorithms which has been originally developed by Runge,
and Danielson and Lanczos which is much faster than the original DFT algorithm.
J.W. Cooley rediscovered this technique, which has been called "Fast
Fourier Transform" (FFT) since then.
Last Update: 2006-Jšn-17