On the probability distributions of spectrogram coefficients for correlated gaussian process

Julien Huillery (1) , Fabien Millioz (1) , Nadine Martin (1)

1 LIS - Laboratoire des images et des signaux

This paper deals with the probability distribution of spectrogram coefficients related to a correlated centered Gaussian process. It is shown that the windowing operation and the presence of correlation between input samples may introduce heteroscedaticity and correlation between the real and imaginary parts of the Short Time Fourier Transform. The impact of this phenomenon on spectrogram distribution is evaluated in terms of deviation from the chi-square distribution. A numerical method is provided to calculate the probability density function of the spectrogram coefficients and deviation from the chi-square distribution is evaluated using the Kullback-Liebler divergence. This measure of deviation is used to control the validity of a chi-square approximation.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Julien Huillery, Fabien Millioz, Nadine Martin. On the probability distributions of spectrogram coefficients for correlated gaussian process. IEEE international Conference on Acoustic, Speech and Signal Processing, May 2006, Toulouse, France. pp.III-436-439. ⟨hal-00301405⟩