Similarity Properties for Two Versions of 1D-, 2D-, 3D-, and ND-Infinite Hartley Transform (IHT)

Abstract

This paper presents similarity properties for two versions of one-dimensional, two-dimensional, three-dimensional and N-dimensional Infinite Hartley Transforms. There exist 2 variants congeneric to the definitions of this transform in multidimensions. The similarity properties are defined and derived separately for these chronicles of the IHT. The habitude of the Similarity properties lie in computing the temporal-domain signal from its frequency-domain peas in a pod or contrariwise from a known IHT pair kindred to the two variants and this helps in the reparatory of time and outlay that are involved in veritably doing the integration. These properties can be used in the field of Multidimensional Signal Processing and Video Processing where there is a doggedness of bumping into signals having the same shape in the temporal- and frequency-domains.