Is Periodic Convolution Same as Circular Convolution?

Question

I know exactly what is periodic convolution. But i don't know if circular convolution means to be the same thing!

Answer 1

You did not give specific details on how you define periodic or circular. Assuming standard definitions, the answer is yes.

Standard infinite-support data is treated with standard convolution. When the support is finite, the "outer unknown samples" require assumptions.

Zero-valued outside samples is a common assertion. Another option, often used with Fourier or wavelet transforms, consists in arranging finite-support data on a ring or torus, the first sample following the last one.

It is often termed periodic, cyclic or circular, with a similar meaning.