Multidimensional discrete convolution: Difference between revisions

Revision as of 20:18, 19 December 2020

Revision as of 17:12, 5 February 2021

Line 92:

<math>x(n_1,n_2,...,n_M) = x(n_1)x(n_2)...x(n_M)</math>

Some readily recognizable separable signals include the unit step function, and the delta-dirac-delta impulse function.

<math>u(n_1,n_2,...,n_M)=u(n_1)u(n_2)...u(n_M)</math> (unit step function)

<math>\delta(n_1,n_2,...,n_M)=\delta(n_1)\delta(n_2)...\delta(n_M)</math> (delta-dirac-delta impulse function)

Convolution is a linear operation. It then follows that the multidimensional convolution of separable signals can be expressed as the product of many one-dimensional convolutions. For example, consider the case where ''x'' and ''h'' are both separable functions.