DFT for something similar to convolution
You might be looking for the convolution property of the DFT. If $z[n] = x[n] * y[n]$, where $*$ represents circular convolution, then $Z[k] = X[k] Y[k]$, where $Z[k]$ is the DFT of $z[n]$ and so on. 

This property is used in fast convolution techniques like overlap-save to implement convolution in $O(N \log N)$ time instead of the $O(n^2)$ time required by direct implementation of the convolution sum.