Signal decomposition and reconstruction using complex exponential models
Signal decomposition and reconstruction using complex exponential models
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DOI：
10.1016/j.ymssp.2013.06.037
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发表时间：
2013-11-01
影响因子：
8.4
通讯作者：
Li, Hua-Jun
中科院分区：
文献类型：
--
作者：
Hu, Sau-Lon James;Yang, Wen-Long;Li, Hua-Jun
本文的主题是信号的分解和重构，而不是特定的或限于系统识别。在处理非周期性阻尼信号时，经常使用基于Prony的技术-将信号分解为真实的和/或复值指数分量。从本质上讲，Prony方法的推导是基于高阶齐次差分方程。本文提出了一种用一阶矩阵齐次差分方程（状态空间模型）代替高阶齐次差分方程的方法。虽然所提出的方法和Prony的方法在理论上似乎是相同的，本文表明，他们是截然不同的关键数值问题，包括空调和稳定性。虽然Prony的方法对采样率和舍入误差非常敏感，但所提出的方法不敏感。虽然Prony的方法在处理嵌入在信号中的噪声时有困难，但所提出的方法可以适当地处理含噪信号，因为它通过使用截断奇异值分解具有内置的噪声抑制机制。Prony方法需要求解高阶多项式的根，这是一个典型的病态问题，而本文方法完全避免了这一问题，并且本文方法也适用于间歇信号，通过重构可以很好地恢复间歇信号中缺失的部分。(C)2013爱思唯尔有限公司保留所有权利。
The theme of this paper is signal decomposition and reconstruction, not specific for or limited to system identification. In dealing with aperiodic damped signals, Prony-based techniques - which decompose a signal into real- and/or complex-valued exponential components - are often utilized. In essence, the derivation of Prony's method has been based on a high order homogeneous difference equation. In this paper, an alternative approach that uses a first-order matrix homogenous difference equation (state-space model) to replace the high order homogenous difference equation is advocated. Although the proposed method and Prony's method appear to be theoretically identical, this paper shows that they are drastically different over crucial numerical issues, including conditioning and stability. While Prony's method is very sensitive to sampling rate and round-off error, the proposed method is not. While Prony's method has trouble to deal with noise embedded in the signal, the proposed method can handle noisy signals properly because it has a build-in noise rejection mechanism via the usage of truncated singular value decomposition. While root-finding of a high order polynomial - a classical ill-conditioned problem - is a required step in Prony's method, the proposed method completely avoids it. The proposed method is also applicable to intermittent signals, and can recover the missing parts of intermittent signals nicely through reconstruction. (C) 2013 Elsevier Ltd. All rights reserved.