2020/07/27 by Bruno Scalzo, Scalzo, Bruno, Ljubiša Stanković +3
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Image and Signal Denoising Methods #Machine Fault Diagnosis Techniques #Signal Processing (eess.SP) #Spectral Theory (math.SP) #Statistics Theory (math.ST) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2007.13855
openalex publication_date 2020/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A class of multivariate spectral representations for real-valued\nnonstationary random variables is introduced, which is characterised by a\ngeneral complex Gaussian distribution. In this way, the temporal signal\nproperties -- harmonicity, wide-sense stationarity and cyclostationarity -- are\ndesignated respectively by the mean, Hermitian variance and pseudo-variance of\nthe associated time-frequency representation (TFR). For rigour, the estimators\nof the TFR distribution parameters are derived within a maximum likelihood\nframework and are shown to be statistically consistent, owing to the\nstatistical identifiability of the proposed distribution parametrization. By\nvirtue of the assumed probabilistic model, a generalised likelihood ratio test\n(GLRT) for nonstationarity detection is also proposed. Intuitive examples\ndemonstrate the utility of the derived probabilistic framework for spectral\nanalysis in low-SNR environments.\n