Unified approach to noise analysis in the Wigner distribution and spectrogram

An analysis of time-frequency representations of noisy signals is performed. Using the method for time-frequency signal analysis which was recently defined by Stankovic (the S-method), the influence of noise on the two most important distributions (spectrogram and Wigner distribution) is analyzed in unified manner. It is also shown that, for signals whose instantaneous frequency is not constant, an improvement over the spectrogram and the Wigner distribution performances in a noisy environment may be achieved using the S-method. The expressions for mean and variance are derived. Results are given for several illustrative and numerical examples.