Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing

The Journal of Engineering

Ioannis Paraskevas¹  Maria Barbarosou²  Edward Chilton³ 

[1] Academic Group of Engineering, Sports and Sciences, Centre for Advanced Performance Engineering (CAPE), University of Bolton, Bolton BL3 5AB, Lancashire, UK;Department of Electronics, Electric Power, Telecommunications, Hellenic Air Force Academy, Dekelia Air Base, Tatoi 13671, Greece;Faculty of Engineering and Physical Sciences, Centre for Vision, Speech and Signal Processing (CVSSP), University of Surrey, Guildford Surrey GU2 7XH, UK

关键词: phase unwrapping;    forward transforms;    Fourier counterpart;    power spectral density function;    mathematical transformation;    Fourier transform;    Fourier phase spectrum;    signal phase content encapsulation;    time-shift property;    Hartley transform;    phase spectral processing;    product-convolution relationship;    inverse transforms;    wrapping ambiguities;    short-time analysis;    whitened Hartley spectrum;   

DOI  :  10.1049/joe.2014.0350

学科分类：工程和技术（综合）

来源: IET

【 摘 要 】

The Hartley transform is a mathematical transformation which is closely related to the better known Fourier transform. The properties that differentiate the Hartley Transform from its Fourier counterpart are that the forward and the inverse transforms are identical and also that the Hartley transform of a real signal is a real function of frequency. The Whitened Hartley spectrum, which stems from the Hartley transform, is a bounded function that encapsulates the phase content of a signal. The Whitened Hartley spectrum, unlike the Fourier phase spectrum, is a function that does not suffer from discontinuities or wrapping ambiguities. An overview on how the Whitened Hartley spectrum encapsulates the phase content of a signal more efficiently compared with its Fourier counterpart as well as the reason that phase unwrapping is not necessary for the Whitened Hartley spectrum, are provided in this study. Moreover, in this study, the product–convolution relationship, the time-shift property and the power spectral density function of the Hartley transform are presented. Finally, a short-time analysis of the Whitened Hartley spectrum as well as the considerations related to the estimation of the phase spectral content of a signal via the Hartley transform, are elaborated.

【 授权许可】

CC BY