多元实值非平稳信号的概率谱分析
A Probabilistic Spectral Analysis of Multivariate Real-Valued Nonstationary Signals
摘要：
引入了一类实值非平稳随机变量的多元谱表示，其特征为一般复高斯分布。通过这种方式，时间信号特性-谐波性，广义平稳性和循环平稳性-分别由相关的时间-频率表示（TFR）的平均值，埃尔米特方差和伪方差指定。为了严格起见，TFR分布参数的估计量是在最大似然框架内得出的，并且由于所提出的分布参数化的统计可识别性，在统计上是一致的。借助于假设的概率模型，还提出了一种用于非平稳检测的广义似然比检验（GLRT）。直观的例子表明，在低信噪比环境下的频谱分析的概率框架的效用。
英文摘要：
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity, wide-sense stationarity and cyclostationarity -- are designated respectively by the mean, Hermitian variance and pseudo-variance of the associated time-frequency representation (TFR). For rigour, the estimators of the TFR distribution parameters are derived within a maximum likelihood framework and are shown to be statistically consistent, owing to the statistical identifiability of the proposed distribution parametrization. By virtue of the assumed probabilistic model, a generalised likelihood ratio test (GLRT) for nonstationarity detection is also proposed. Intuitive examples demonstrate the utility of the derived probabilistic framework for spectral analysis in low-SNR environments.
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