In this research, we highlight the importance of the background noise properties in the context of the vibration- based local damage detection. In the case, when the background noise has Gaussian characteristics, the classical methods for local damage detection can be applied. However, for many real signals the assumption of Gaussian distribution of the noise is not satisfied and one may expect the large impulses that influence the noise char- acteristics. In that case the impulsiveness criteria fail. Since, most of the methods for local damage detection are based on the autocovariance function properly defined for signals with finite second moment, we indicate here the important role of the finite variance of the signal and present a new approach for the assessment of the probabilistic properties of the noise. The methodology is applied for the TF representation of the signals. The problem is illustrated for the simulated signals from exemplary non-Gaussian distribution.