Aspects of the Hartley transform

Known in the signal processing literature mainly as a computational technique, the Hartley transform has proven to possess attributes in the physical world of experiment, especially in optics and microwaves. The Fourier transform, which has constituted the standard approach to spectral analysis, is understood both in the domain of numerical analysis and in the world of natural phenomena, gaining its central significance from the ubiquity of sinusoidal natural behavior; it also gains appeal from the convenience offered by complex variable analysis, which is a basic part of technical education. Computers, however, prefer real numbers, an attribute that first opened a niche for the Hartley transform. As applications have multiplied, and others open up, it will be helpful to understand the Hartley idea from more than one point of view. Several topics, including multidimensional transforms, the complex generalization, and microwave phase measurement by amplitude measurement only, are discussed with the intention of throwing light on the numerical and physical relationships between the Hartley and Fourier transforms