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Signals and Systems by Smarajit Ghosh

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11.8.1 Properties of FFT

The N point DFT sequence is given by

 

image

 

which is known as the twiddle factor and it exhibits symmetry and periodicity properties.

11.8.1.1 Periodicity property of WN

This property states that image

Proof:

WN is represented by image

 

image

 

Since ej2π = 1, we have from Eq. (11.97)

 

11.8.1.2 Symmetry property

This property states ...

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