Circular Convolution Property

Circular Convolution Using DFT and IDFT

The convolution theorem for the discrete-time Fourier transform (DTFT) indicates that a convolution of two sequences can be obtained as the inverse transform of the product of the individual transforms. An important simplification occurs when one of sequences is N-periodic, denoted here by y_N because DTFT{y_N} is non-zero at only discrete frequencies, and therefore so is its product with the continuous function DTFT{x} That leads to a considerable simplification of the inverse transform.

Then the convolution can be written as:

The step-by-step values for the provided input is shown at the bottom of the page:

Circular Convolution Using DFT and IDFT

Enter the first sequence :

Enter the second sequence :

Input sequence :

Impulse sequence :

Ouput sequence :

x(n) and h(n) :

Multiply the below sequences :

y(n) :