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Convolution is a linear operation. It then follows that the multidimensional convolution of separable signals can be expressed as the product of many one-dimensional convolutions. For example, consider the case where ''x'' and ''h'' are both separable functions.
<math>x(n_1,n_2)**h(n_1,n_2)=\sum_{k_1=-\infty}^{\infty} \sum_{k_2=-\infty}^{\infty} h(k_1,k_2)x(n_1-k_1,n_2-k_2)</math>
By applying the properties of separability, this can then be rewritten as the following:
<math>x(n_1,n_2)**h(n_1,n_2)=\bigg(\sum_{k_1=-\infty}^{\infty} h(k_1)x(n_1-k_1)\bigg)\bigg(\sum_{k_2=-\infty}^{\infty}h(k_1)x(n_1-k_1)\bigg)</math>
===Row-Column Decomposition===
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