Multidimensional discrete convolution

In signal processing, multidimensional convolution refers to the mathematical operation between two functions f and g of n-dimensions that produces a third function, also of n-dimensions.

Definition

Problem Statement & Basics

Motivation & Applications

Row-Column Decomposition with Separable Signals

Separable Signals

A signal is said to be separable if it can be written as the product of multiple 1-Dimensional signals ^[1]. Mathematically, this is expressed as the following:

${\displaystyle x(n_{1},n_{2},...,n_{M})=x(n_{1})x(n_{2})...x(n_{M})}$ 

Overlap and Add and Overlap and Save

The Helix Transform

References

1. Dudgeon, Dan; Mersereau, Russell (1983), Multidimensional Digital Signal Processing, Prentice-Hall, p. 8