The Fourier Transform provides the means of transforming a signal defined in the time domain into one defined in the frequency domain (see Tutorial 2 on time and frequency representation). When a function is evaluated by numerical procedures, it is always necessary to sample it in some fashion (refer to Tutorial 3 on Sampling and Aliasing).
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http://www.cage.curtin.edu.au/mechanical/info/vibrations/tut4.htm
06/28/2002