Signals and Systems

11.8.1 Properties of FFT

The N point DFT sequence is given by

 

 

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

11.8.1.1 Periodicity property of W_N

This property states that

Proof:

W_N is represented by

 

 

Since e^−j2π = 1, we have from Eq. (11.97)

 

11.8.1.2 Symmetry property

This property states ...