HARTLEY TRANSFORM: AN ELEGANT TOOL FOR SOUND AND VIBRATION ANALYSIS

摘要

The objective of this paper is to introduce Hartley's purely real variant of the Fourier transform to sound and vibration analysis. The discrete implementation of the Hartley transform involves fewer real multiplications than that of the complex fast Fourier transform. Considerable savings in time result from the elimination of redundant calculations which occur with the numerical evaluation of the Fourier transform of real data. This implies that during the computation of frequency domain quantities like auto- and cross-spectra, coherence, spectral density matrices associated with multiple input and output systems, etc., the Hartley transform saves a considerable amount of time. The Hartley transform can also be readily used in such diverse areas as optics and thermodynamics. As a representative example from the sound and vibration area, a detailed derivation of an expression for measuring sound intensity using the two-microphone technique with the Hartley transform is presented here. Certain ideas associated with the numerical simulation of sound fields using spectral methods that take advantage of an identical forward and backward Hartley transform algorithm are also presented.