Mean value jump detection using wavelet decomposition

The problem of detecting a mean value jump of a stationary random process by means of the wavelet transform (WT) is studied. This is significant for general nonstationarity detection. The properties of the continuous and discrete transforms are investigated, and the SNR expression is derived. It is shown that the Haar wavelet is optimum with respect to this criterion, but the discrete wavelet transform (DWT) is shown to have some major drawbacks for this application. Various detection strategies are described and illustrated, showing that the WT is a powerful tool, even with very small SNR