Hardy–Sobolev derivatives of phase and amplitude, and their applications
Hardy–Sobolev derivatives of phase and amplitude, and their applications
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DOI：
10.1002/mma.2632
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发表时间：
2012-11
影响因子：
2.9
通讯作者：
P. Dang;Tao Qian;Yan Yang
中科院分区：
文献类型：
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作者：
P. Dang;Tao Qian;Yan Yang
在时频分析中，有基本公式表示信号的傅里叶频率s的均值和方差，最初定义在傅里叶频域中，根据对密度的积分|s（t）的值|2在时间域在文献中，现有的公式只适用于光滑信号，因为它是涉及到的信号的相位和幅度的经典导数。协方差的两种表示也依赖于经典导数，因此是限制性的。在这项基础研究中，通过引入一种新类型的衍生物，称为Hardy-Sobolev衍生物，我们将公式扩展到通常没有经典衍生物的Sobolev空间中的信号。我们还研究了相应的公式周期（无限离散）和有限离散信号。版权所有© 2012约翰威利父子有限公司.
In time‐frequency analysis, there are fundamental formulas expressing the mean and variance of the Fourier frequency of signals, s, originally defined in the Fourier frequency domain, in terms of integrals against the density | s(t) | 2 in the time domain. In the literature, the existing formulas are only for smooth signals, for it is the classical derivatives of the phase and amplitude of the signals that are involved. The two representations of the covariance also rely on the classical derivatives and thus are restrictive. In this fundamental study, by introducing a new type of derivatives, called Hardy–Sobolev derivatives, we extend the formulas to signals in the Sobolev space that do not usually have classical derivatives. We also investigate the corresponding formulas for periodic (infinite discrete) and finite discrete signals. Copyright © 2012 John Wiley & Sons, Ltd.