Signal decomposition and analysis via extraction of frequencies
Signal decomposition and analysis via extraction of frequencies
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DOI：
10.1016/j.acha.2015.01.003
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发表时间：
2016-01-01
影响因子：
2.5
通讯作者：
Mhaskar, H. N.
中科院分区：
文献类型：
--
作者：
Chui, Charles K.;Mhaskar, H. N.
时频分析是信号处理的核心，具有对成像应用等更高维度的标准适应性。然而，尽管平稳信号的理论、方法和算法已经发展得很好，但非平稳信号的数学分析几乎不存在。对于定义在时域R上的实值信号，计算其瞬时频率（IF）的经典方法是通过希尔伯特变换考虑其复（或解析）信号扩展的幅度频率调制（AM-FM）公式。在Huang等人的一篇受欢迎的论文中，引入了所谓的经验模式分解（EMD）方案，以将这样的信号分离为多个固有模式函数（IMF）的和，其中缓慢振荡信号作为余数，使得可以通过将每个IMF扩展为AM-FM信号分量来计算给定信号的多于一个的IF。基于连续小波变换（CWT），同步压缩变换（SST）的概念由Daubechies和Maes在1996年提出，并由Daubechies，Lu和Wu（DLW）在2011年的论文中进一步发展，提供了另一种方法来提取R上信号的多个IF。此外，通过引入自适应谐波模型（AHM）的一系列相当严格的条件，DLW论文还导出了一种理论，用于根据该模型估计信号分量，通过使用具有SST估计的IF。我们目前的论文的目的是引入另一种数学理论，沿着的严格方法和计算方案，以实现比SST方法更雄心勃勃的目标，首先从源信号中提取多项式趋势，然后根据限制较少的AHM模型计算信号分量的确切数量，然后获得信号分量的IF和瞬时幅度（IA）的更好估计，最后从（盲）源信号中分离信号分量。此外，我们的计算方案可以实现在近实时，我们的数学理论有直接的扩展到多变量设置。(C)2015 Elsevier Inc. All rights reserved.
Time-frequency analysis is central to signal processing, with standard adaptation to higher dimensions for imaging applications, and beyond. However, although the theory, methods, and algorithms for stationary signals are well developed, mathematical analysis of non-stationary signals is almost nonexistent. For a real-valued signal defined on the time-domain R, a classical approach to compute its instantaneous frequency (IF) is to consider the amplitude frequency modulated (AM-FM) formulation of its complex (or analytic) signal extension, via the Hilbert transform. In a popular paper by Huang et al., the so-called empirical mode decomposition (EMD) scheme is introduced to separate such a signal as a sum of finitely many intrinsic mode functions (IMFs), with a slowly oscillating signal as the remainder, so that more than one IFs of the given signal can be computed by extending each IMF to an AM-FM signal component. Based on the continuous wavelet transform (CWT), the notion of synchrosqueezing transform (SST), introduced by Daubechies and Maes in 1996, and further developed by Daubechies, Lu, and Wu (DLW) in a 2011 paper, provides another approach to extract more than one IFs of the signal on R. Furthermore, by introducing a list of fairly restrictive conditions on the adaptive harmonic model (AHM), the DLW paper also derives a theory for estimating the signal components according to this model, by using the IFs with estimates from the SST.The objective of our present paper is to introduce another mathematical theory, along with rigorous methods and computational schemes, to achieve a more ambitious goal than the SST approach, first to extract the polynomial-like trend from the source signal, then to compute the exact number of signal components according to a less restrictive AHM model, then to obtain better estimates of the IFs and instantaneous amplitudes (IAs) of the signal components, and finally to separate the signal components from the (blind) source signal. Furthermore, our computational scheme can be realized in near-real-time, and our mathematical theory has direct extension to the multivariate setting. (C) 2015 Elsevier Inc. All rights reserved.