Suppose \(\mathbb{K}\) be either \(\mathbb{C}\) or \(\mathbb{R}\). The convolution of two vectors \(x,y\in \mathbb{K}^n\) is given by
\[ x\ast y (k) = \sum_{j\in \mathbb{Z}_n}x(j)y(k-j) = \sum_{j\in \mathbb{Z}_n}x(k-j)y(j). \]Suppose \(\mathbb{K}\) be either \(\mathbb{C}\) or \(\mathbb{R}\). The convolution of two vectors \(x,y\in \mathbb{K}^n\) is given by
\[ x\ast y (k) = \sum_{j\in \mathbb{Z}_n}x(j)y(k-j) = \sum_{j\in \mathbb{Z}_n}x(k-j)y(j). \]