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Z-domain counterpart to prony's method for exponential-sinusoidal decomposition

机译:Prony指数正弦分解方法的Z域对应物

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摘要

Prony's method has applications in exponential sinusoidal modelling, parametric modelling, filter design, system modelling and system identification. Similarly to Pade approximation, Prony's method and refinements thereof are major tools for statistical signal analysis, system auto-regressive moving average (ARMA) modelling and least-squares digital filter design. In this study, a z-domain counterpart to Prony's method is proposed as a spectral analysis approach to exponential-sinusoidal decomposition in the presence of noise contamination. The approach is particularly effective in the case where the signal components have 'well behaved' frequencies, meaning that they are multiples of the fundamental frequency. Spectral weighting is applied to power spectra over the z-plane. Spectral peaks of signals contaminated by noise are used to estimate the amplitude, frequency, damping and phase of damped sinusoidal components. The present approach requires no a priori knowledge of the number of damped sinusoidal components present in the contaminated signal, and hence no knowledge of the system order. As expected, however, the analysed signal duration should be long enough to reveal signal properties in the presence of noise. In the case where signal components are not well behaved, spectral leakage would necessitate windowing and higher resolution frequency analysis in order to identify the successive components with improved accuracy
机译:Prony的方法可用于指数正弦建模,参数建模,滤波器设计,系统建模和系统识别。与Pade近似类似,Prony的方法及其改进是统计信号分析,系统自回归移动平均(ARMA)建模和最小二乘数字滤波器设计的主要工具。在这项研究中,提出了Prony方法的z域对应物,作为在存在噪声污染的情况下进行指数正弦分解的频谱分析方法。该方法在信号成分具有“良好表现”频率的情况下特别有效,这意味着它们是基频的倍数。频谱加权应用于z平面上的功率谱。被噪声污染的信号的频谱峰值用于估计阻尼正弦分量的幅度,频率,阻尼和相位。本方法不需要对污染信号中存在的阻尼正弦分量的数量有先验知识,因此不需要系统次序的知识。但是,正如预期的那样,分析的信号持续时间应足够长,以在存在噪声的情况下揭示信号特性。在信号成分表现不佳的情况下,频谱泄漏将需要开窗和更高分辨率的频率分析,以便以更高的精度识别出连续的成分

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    《Signal Processing, IET》 |2010年第5期|p.537-547|共11页
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