Multidimensional discrete convolution: Difference between revisions

Revision as of 09:24, 1 May 2021

Revision as of 16:48, 12 May 2021

Line 290:

===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_{M \times N}</math> and <math>Y_{K \times L}</math>, which results in an output <math>Z_{(M \times N-1)+( K + 1)\times(N L- 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>