Discrete fourier transform circular symmetry

1. What is the symmetry property of discrete Fourier transform?
2. Does DFT support circular convolution?
3. Is DFT symmetrical?
4. What is circular shift in DFT?

What is the symmetry property of discrete Fourier transform?

Symmetry Property of Discrete-Time Fourier Transform

i.e., the real part of DTFT Xr(ω) is an even function of 𝜔, i.e., it has even symmetry property. Therefore, the imaginary part of DTFT Xi(ω) is an odd function of 𝜔, i.e., it has odd symmetry property.

Does DFT support circular convolution?

Obviously, convolution via DFT is not exactly the same as linear convolution. It is called circular convolution. The convolution is circular because of the periodic nature of the DFT sequence. Recall that an N-point DFT of an aperiodic sequence is periodic with a period of N.

Is DFT symmetrical?

And without going into mathematical details, DFT of real valued function is symmetric, i.e. resultant Fourier function has both real and imaginary parts which are mirror images with respect to 0 frequency component.

What is circular shift in DFT?

Circular Frequency Shift

The multiplication of the sequence xn with the complex exponential sequence ej2Πkn/N is equivalent to the circular shift of the DFT by L units in frequency.