Nonstationary and stationary noise

Many man made and natural noises in nature are nonstationary, however most methods that have been devised to study noises, theoretically or experimentally, have been devised for the stationary situations. We have developed a number of methods to study noises that are nonstationary. We use the Wigner spectrum and other time-frequency representations to represent time-varying noises. These representations can be thought of as a generalization of the standard power spectrum. In this paper we study simple models of nonstationary noises and obtain the Wigner spectrum numerically from realizations of the noises and also by direct calculation. We show that for our test cases the Wigner spectrum clearly shows the nonstationarities of the noise. We also present a method to generate nonstationaxy white noise that has very different behavior than the standard white Gaussian noise.