Multidimensional discrete convolution: Difference between revisions

Revision as of 00:23, 8 November 2015

Revision as of 00:26, 8 November 2015

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==Overlap and Add and Overlap and Save==

Another method to perform multidimensional convolution is the '''overlap and add''' approach. This method helps reduce the computational complexity often associated with multidimensional convolutions due to the vast amounts of data inherent in modern day digital systems. <ref>{{cite journal|last1=Fernandez|first1=Joseph|last2=Kumar|first2=Vijaya|title=Multidimensional Overlap-Add and Overlap-Save for Correlation and Convolution|journal=IEEE|date=Sept. 2013|issue=Image Processing (ICIP)|pages=509-513|doi=10.1109/ICIP.2013.6738105}}</ref>{{Multiple issues|{{dead end|date=November 2015}}{{orphan|date=November 2015}}{{one source|date=November 2015}}{{technical|date=November 2015}}}} For example, consider a two-dimensional convolution using a direct computation:

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