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introduction Discrete Fourier Transform
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The Discrete Fourier Transform (DFT) of a signal may be defined by
Where ` ' means is defined as'' or
equals by definition'', and
The inverse DFT (the IDFT) is given by
In the signal processing literature, it is common to write the DFT and its inverse in the more pure form below, obtained by setting in the previous definition:
Where denotes the input signal at time (sample) , and denotes the th spectral sample. This form is the simplest mathematically, while the previous form is easier to interpret physically.