Multidimensional discrete convolution: Difference between revisions

Revision as of 23:48, 7 November 2015

Revision as of 23:52, 7 November 2015

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Instead of performing convolution on the blocks of information in their entirety, the information can be broken up into smaller blocks resulting in smaller FFTs, less computational complexity, and less storage needed. This can be expressed mathematically as follows:

<math> x(n_1, n_2) = \sum_{i=1}^{L_1} \sum_{j=1}^{L2L_2}xx_{ij}(n_1, n_2)</math>

where <math>x(n_1, n_2)</math> represents the input signal, which is a summation of <math>L_1L_2</math> block segments.

To produce the output signal, a two-dimensional convolution is performed:

<math>y(n_1,n_2) = x(n_1, n_2) ** h(n_1, n_2)</math>

Substituting in for <math>x(n_1, n_2)</math> results in the following:

<math>y(n_1,n_2) = \sum_{i=1}^{L_1} \sum_{j=1}^{L_2}x_{ij}(n_1, n_2)** h(n_1, n_2)</math>

This convolution

==The Helix Transform==