Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Bivariate Data Time Series Fourier Transformation Introduction  
See also: time and frequency, Fourier series, FFT  
Fourier Transformation  IntroductionThe 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: For transforming the signal back into the time domain the inverse Fourier transform can be applied: 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 realtime 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.


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