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Discrete Fourier Transform, Study notes of Signals and Systems Theory

introduction Discrete Fourier Transform

Typology: Study notes

2014/2015

Uploaded on 06/10/2015

saagar91
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Discrete Fourier Transform:-
The Discrete Fourier Transform (DFT) of a signal may be dened by
Where ` ' means ``is dened as'' or ``equals by denition'', 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 denition:
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.

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Discrete Fourier Transform:-

The Discrete Fourier Transform (DFT) of a signal may be defined by

Where ` ' means is defined as'' orequals 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.