A New Avenue to the Reciprocity Axioms of Multidimensional DHT Through Those of the Multidimensional DFT

Abstract

The main objective of this paper is to acquaint the reader with a trailblazing pike into the reciprocity axioms of the multidimensional discrete Hartley transform (DHT) through the multidimensional discrete Fourier transform (DFT). Spin-offs for the reciprocity axioms of multidimensional DHT are tendered through the reciprocity axioms of the multidimensional DFT. This is due to the mathematical hookup betwixt the DFT and DFT. DHT is a real transform, whilst the DFT is a complex transform. Real transforms are posthaste in implementation in contrast to the complex transforms. Ergo, the axioms deduced for the reciprocity of multidimensional DHT in this paper, can be used in real time for the implementation of reciprocity axioms of multidimensional DFT at a brisk pace, by half of the cent percentage than their actual use. Thence, the axioms for multidimensional DHT can be used in real-time applications that use multidimensional DFT such as digital video processing, colour image processing.