论文标题
多变量实用值非平稳信号的概率光谱分析
A Probabilistic Spectral Analysis of Multivariate Real-Valued Nonstationary Signals
论文作者
论文摘要
引入了一类用于实价非平稳随机变量的多元光谱表示，其特征在于一般的复杂高斯分布。这样，时间信号属性（谐波，宽宽的平稳性和环化性）分别由相关时频表示（TFR）的平均值，遗产差异和伪变异来指定。对于严格，TFR分布参数的估计器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识别性，因此被证明在统计上是一致的。由于假定的概率模型，还提出了用于非平稳性检测的广义似然比测试（GLRT）。直观的示例证明了在低SNR环境中派生的概率框架用于光谱分析的实用性。
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.
