A fast Hartley transform implementation on a TMS320 series DSP

Abstract

The Fourier transform is a ubiquitous tool found in such diverse fields such as acoustics, optics, seismology, telecommunications and signal processing. Yet, for most numerical calculations, it is usually the Discrete Fourier Transform (DPT) which is performed. This is due to the prevalent usage of, as opposed to analog computers, digital computers which internally represent continuous functions in terms of discrete approximations.

The calculation of the DFT appeared to be quite impractical for most applications, until the development of the Fast Fourier transform (FFT) algorithm by Cooley . The FFT reduced the time to compute the DFT from an order of n² to n log n, where n is the number of discrete points.

The FFT gained wider usage with the recent developments of single-chip VLSI Digital Signal Processors (DSPs). DSPs are basically microprocessors enhanced with features suitable for Digital Signal Processing. Although, the implementation of the FFT in DSPs have been quite widespread, for a lesser known equivalent algorithm, the Fast Hartley Transform, the situation has been dissapointing.

This paper briefly introduces the Hartley Transform andits discrete counterpart the Discrete Hartley Transform (DHT), We then discuss the development of a FFT-like algorithm for the Hartley transform (i.e. Fast Hartley Transform). We then present an implementation of the FHT on a TMS32010 series DSP.