Suppose \(\mathbb{K}\) be either \(\mathbb{C}\) or \(\mathbb{R}\). Let \(x,y\in \mathbb{K}^n\). The discrete Fourier transform satisfies
\[ \widehat{x\ast y}_k=\hat{x}_k\hat{y}_k \]for all \(k\in \{1,\ldots ,n\}\).
Suppose \(\mathbb{K}\) be either \(\mathbb{C}\) or \(\mathbb{R}\). Let \(x,y\in \mathbb{K}^n\). The discrete Fourier transform satisfies
\[ \widehat{x\ast y}_k=\hat{x}_k\hat{y}_k \]for all \(k\in \{1,\ldots ,n\}\).