Multidimensional discrete convolution: Difference between revisions

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The overlap and save method is very similar to the overlap and add methods with a few notable exceptions. The overlap-add method involves a linear convolution of discrete-time signals, whereas the overlap-save method involves the principle of circular convolution. In addition, the overlap and save method only uses a one-time zero padding of the impulse response, while the overlap-add method involves a zero-padding for every convolution on each input component. Instead of using zero padding to prevent time-___domain aliasing like its overlap-add counterpart, overlap-save simply discards all points of aliasing, and saves the previous data in one block to be copied into the convolution for the next block.

In one dimension, the performance and storage metric differences between the two methods is minimal. However, in the multidimensional convolution case, the overlap-save method is preferred over the overlap-add method in terms of speed and storage abilities.<ref>{{Cite journal|url = |title = High-Speed Multidimensional Convolution|last = Kim|first = Chang|date = May 1980|journal = IEEE Transactions on Pattern Analysis and Machine Intelligence|doi = |pmid = |access-date =10.1109/tpami.1980.4767017 |last2 = Strintzis|first2 = Michael}}</ref> Just as in the overlap and add case, the procedure invokes the two-dimensional case but can easily be extended to all multidimensional procedures.

===Breakdown of Procedure===