Fast Fourier Transform commands compute the discrete Fourier transform (DFT) and its inverse using a fast Fourier transform (FFT) algorithm.  Direct discrete Fourier transform converts a set of time samples to coefficients of a finite combination of complex sinusoids, ordered by their frequencies. It can be said that data in the time domain is converted to data in the frequency domain. Fourier transform is an important tool in many areas of science and engineering.

How To

Direct Transform:
Run: Statistics→Time Series →Fast Fourier Transform - Direct...
Inverse Transform:
Run: Statistics→Time Series →Fast Fourier Transform - Inverse...

Select variables containing the real and imaginary values of time series. Variable with imaginary values is optional; when omitted, imaginary values are assumed to be zero.

Results

Direct Transform:
Discrete Fourier transform is computed as:

, where  is discrete Fourier series.

Inverse Transform:
Inverse discrete Fourier transform is computed as

, where  is sampled spectrum.

 

References

Brigham, E. (1988), The Fast Fourier Transform And Its Applications. Englewood Cliffs, Prentice-Hall, NJ. Burg J.P. (1975)