Fourier and Hartley transforms - A mathematical twin

The Hartley transform, using yet another set of orthogonal functions, is purely real and fully equivalent to the well-known Fourier transform. It is an offshoot of the Fourier transform with the same physical significance as that of its progenitor. The fact that the Fourier and Hartley transforms contain the same information at each frequency combined with that these two transforms yield identical amplitude and phase paves the way for phrasing them to be a mathematical twin. The Hartley transform has some computational advantages over the Fourier transform and therefore can be an ideal alternative to the Fourier transform for all its applications. Some salient features of this transform which is emerging as an important tool in the field of digital signal processing are incorporated herein.