The Fourier transform is widely used for
converting any mathematical description of a time domain waveform into the frequency
domain equivalent. As such it can be viewed as a generalization of the Fourier series
expansion. There is also an inverse Fourier transform which
will convert from the frequency domain to the time domain.
The Fourier transform X(f) of a time function x(t) is defined as:

and the inverse Fourier transform is given by:

A more detailed analyis of Fourier transforms can be found in Haykin (1989).
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