Multidimensional discrete convolution: Difference between revisions

Revision as of 10:14, 3 August 2019

Revision as of 23:09, 5 September 2019

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===Multidimensional Convolution with One-Dimensional Convolution Methods===

To understand the helix transform, it is useful to first understand how a multidimensional convolution can be broken down into a one-dimensional convolution. Assume that the two signals to be convolved are <math>X_{MxNM \times N}</math> and <math>Y_{K x\times L}</math>, which results in an output <math>Z_{(MxNM \times N-1)+(KxLK \times L-1)}</math>. This is expressed as follows:

<math>Z(i,j) = \sum_{m=0}^{M-1}\sum_{n=0}^{N-1}X(m,n)Y(i-m, j-n)</math>