Circular convolution of real signal N by N/2 sized complex IFFT

1. How do you find the N point circular convolution?
2. What is circular convolution formula?
3. How do you find circular convolution using DFT?

How do you find the N point circular convolution?

1 Convolution

Since a(m + N) = a(m), the sequence a(m) is periodic with period N. Therefore A(k) = DFT[a(m)] has period N and is determined by A(k) = X(k)Y(k).

What is circular convolution formula?

� From our definition of the circular convolution w[n], W[k] = X[k]H[k], so W[k] = Y [k]. If x[n] and h[n] are sequences of length N, then w[n] has length N, but y[n] has the maximum. length of (2N-1). In order to calculate the N-point DFT of y[n], we first form a periodic sequence.

How do you find circular convolution using DFT?

For two vectors, x and y , the circular convolution is equal to the inverse discrete Fourier transform (DFT) of the product of the vectors' DFTs. Knowing the conditions under which linear and circular convolution are equivalent allows you to use the DFT to efficiently compute linear convolutions.