Recognition of signals from colored noise background in generalized S-transformation domain

We study how to distinguish signals from colored noise in the S-transform (ST) and generalized S-transform (GST) domain. First, the mean ST and GST power spectra of white noise are derived. The result shows that they are related linearly with frequency. Then the local GST power spectrum of colored noise is qualitatively analyzed. It is concluded that the local GST spectrum of colored noise follows chi-square distribution with two degree of freedom. These conclusions are verified by Monte Carle simulation. Based on the above results, a method to distinguish signals from colored noise is proposed, and its effectiveness is proved by synthetic data.