1/f Noise decomposition in random telegraph signals using the wavelet transform

By using the continuous wavelet transform with Haar basis the second-order properties of the wavelet coefficients are derived for the random telegraph signal (RTS) and for the 1/f noise which is obtained by summation of many RTSs. The correlation structure of the Haar wavelet coefficients for these processes is found. For the wavelet spectrum of the 1/f noise some characteristics related to the distribution of the relaxation times of the RTS are derived. A statistical test based on the characterization of the time evolution of the scalogram is developed, which allows to detect non-stationarity in the times τ's which compose the 1/f process and to identify the time scales of the relaxation times where the non-stationarity is localized. The proposed method allows to distinguish noise signals with 1/f power spectral density generated by RTSs, and thus gives informations on the origin of this type of 1/f noise which cannot be obtained using the Fourier transform or other methods based on second-order statistical analysis. The reported treatment is applied to both simulated and experimental signals. The present analysis is based on the McWhorter [1/f Noise and germanium surface properties, in: R.H. Kingstone (Ed.), Semiconductor Surface Physics, University of Pennsylvania Press, Philadelphia, PA, 1957, pp. 207–228] model of low frequency electric noise, and the obtained results are expected to prove especially useful for semiconductor devices.