Noise decomposition in random telegraph signals using the wavelet transform

✍ Scribed by Fabio Principato; Gaetano Ferrante

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 658 KB
• Volume: 380
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2007.02.111

✦ Synopsis

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 t'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: