Application of the fast Hartley transform to industrial noise analysis

Abstract

The application of the fast Hartley transform (FHT) to industrial noise analysis to replace the fast Fourier transform (FFT) is proposed. The Hartley transform of a real‐valued function is also real‐valued. Its evaluation does not involve complex functions and it has the same formula for forward and inverse transform. Thus it has a speed advantage over FFT. The type of FHT algorithm chosen is due to H. V. Sorensen et al. [IEEE Trans. Acoust. Speech Signal Process. ASSP‐33, 1231–1238 (1985)]. As an illustration, the two‐channel FFT signal processor is chosen. The computation of the following functions is repeated: autocorrelation function, cross‐correlation function, power spectrum, and the acoustic intensity of real‐numbered data by replacing the FFT with FHT. A detailed analysis of the time that can be saved in computation by using FHT is made. A key advantage of the Hartley transform technique for large autocorrelation is the use of the same formula for transforming and inverse transforming.