Multidimensional discrete convolution: Difference between revisions

Revision as of 18:09, 7 April 2018

Revision as of 12:24, 4 May 2018

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

<math>x(n_1,n_2,...,n_M)* \overset{M}{\cdots} *h(n_1,n_2,...,n_M)=\bigg[x(n_1)*h(n_2n_1)\bigg]\bigg[x(n_2)*h(n_2)\bigg]...\bigg[x(n_M)*h(n_M)\bigg]</math>

So, when the two signals are separable, the multidimensional convolution can be computed by computing <math>n_M</math> one-dimensional convolutions.