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首页> 外文期刊>The Journal of Engineering >Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing
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Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing

机译：Hartley变换和Whitened Hartley谱作为相谱处理工具的使用

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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 producta??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.
机译：Hartley变换是一种数学变换，与众所周知的Fourier变换密切相关。使Hartley变换与Fourier变换区别开来的特性是，正向和逆向变换是相同的，并且真实信号的Hartley变换是频率的真实函数。源于Hartley变换的Whiteed Hartley频谱是一个有界函数，它封装了信号的相位内容。与傅立叶相位光谱不同，Whitened Hartley光谱的功能不会受到不连续性或环绕模糊性的影响。这项研究提供了一个概述，与傅立叶信号相比，白化哈特利频谱如何更有效地封装信号的相位内容，以及白化哈特利频谱不需要相位解缠的原因。此外，在这项研究中，给出了哈特利变换的乘积，卷积关系，时移特性和功率谱密度函数。最后，阐述了对Whiteed Hartley频谱的短时分析以及与通过Hartley变换估计信号的相位频谱含量有关的注意事项。

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