Multidimensional discrete convolution: Difference between revisions

Revision as of 06:53, 19 June 2016

Revision as of 03:06, 20 June 2016

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<math>y(n_1,n_2)=\sum_{k_1=-\infty}^{\infty} \sum_{k_2=-\infty}^{\infty} h_1(k_1)h_2(k_2)x(n_1-k_1,n_2-k_2)</math>

<math>y(n_1,n_2)=\sum_{k_1=-\infty}^{\infty}h_1(k_1)\Bigg[ \sum_{k_2=-\infty}^{\infty} h_2(k_2)x(n_1-k_1n_2k_1,n_2-k_2)\Bigg]</math>

Thus, the resulting convolution can be effectively calculated by first performing the convolution operation on all of the rows of <math>x(n_1,n_2)</math>, and then on all of its columns. This approach can be further optimized by taking into account how memory is accessed within a computer processor.