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 to calculate the probability density function of the spectrogramcoefficients is provided 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.
