Multidimensional discrete convolution: Difference between revisions

Revision as of 23:52, 7 November 2015

Revision as of 23:56, 7 November 2015

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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)=\bigg[x(n_1)*h(n_1)\bigg]\bigg[x(n_2)*h(n_2)\bigg]</math>

This conclusion can then be extended to the convolution of two ''M''-dimensional signals as follows:

<math>x(n_1,n_2,...,n_M)*...*h(n_1,n_2,n_M)=\bigg[x(n_1)*h(n_2)\bigg]\bigg[x(n_2)*h(n_2)\bigg]...\bigg[x(n_M)*h(n_M)\bigg]</math>

===Row-Column Decomposition===