On the Description of Spectrogram Probabilities With a Chi-Squared Law

Abstract--Given a correlated Gaussian signal, may a chisquared law of probability always be used to describe a spectrogram coefficient distribution? If not, would a "chi-squared description" lead to an acceptable amount of error when detection problems are to be faced in the time-frequency domain? The two questions prompted the study reported in this paper. After deriving the probability distribution of spectrogram coefficients in the context of a non-centred Gaussian correlated signal, the Kullback-Leibler divergence is first used to evaluate to what extent the non-whiteness of the signal and the Fourier analysis window impact the probability distribution of the spectrogram. To complete the analysis, a detection task formulated as a binary hypothesis test is considered. We evaluate the error committed on the probability of false alarm when the likelihood ratio test is expressed with chi-squared laws. From these results, a chi-squared description of the spectrogram distributi...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: J. Huillery, F. Millioz, N. Martin
• Keywords: Chi-squared Description, Spectrogram, Spectrogram Coefficients, TSP 2008