Circular Convolution of Length L of Sequences of Length Greater Than L

1. What is the length of circular convolution?
2. What is the circular convolution of the sequence?
3. What is relation between linear and circular convolution?

What is the length of circular convolution?

The length L ≥ M + K − 1 of the DFT Y[k] = X[k]H[k] corresponds to a circular convolution of length L of the x[n] and h[n] padded with zeros so that both have length L. In such a case the circular and the linear convolutions coincide.

What is the circular convolution of the sequence?

Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT).

What is relation between linear and circular convolution?

The linear convolution of an N-point vector, x , and an L-point vector, y , has length N + L - 1. For the circular convolution of x and y to be equivalent, you must pad the vectors with zeros to length at least N + L - 1 before you take the DFT.