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From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast routine (or FFT), and that the data sets are of length N = 2n, unless noted otherwise. The DFT pair will be written
In this formulation, Y0 represents the average value of the data, the so-called DC term. In addition, |Yn|2 represents the contribution that frequencies near n/N make to total data variance.
(Note: Some FFT routines require that the data first be made complex.)
Experiment with some versions of the FFT available to you, first using a digitised sinusoid as input. Then attempt to duplicate the figure below, comment on variance normalisation.
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definition of trigonometric function #Minimum 100 words accepted#
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