Multidimensional discrete convolution: Difference between revisions

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<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>
 
It is readily seen then that this reduces to the product of two one-dimensional convolutions:
 
<math>x(n_1,n_2)**h(n_1,n_2)=[x(n_1)*h(n_1)][x(n_2)*h(n_2)]</math>
 
===Row-Column Decomposition===