Archivio Istituzionale della RicercaWe have previously presented a method to write equations for the Wigner distribution corresponding to the solution of a linear differential equation. We extend this method to arbitrary time-frequency distributions, the Short Time Fourier Transform, and the wavelet transform. Also, we apply the method to stochastic signals and address a number of applications including Brownian motion. We obtain the Wigner distribution for Brownian motion by solving the Langevin equation and also by using our method. We obtain exact solutions.
Time-frequency characterization of random systems / Galleani, Lorenzo; Cohen, L.. - STAMPA. - 5205:(2003), pp. 21-37. (Intervento presentato al convegno SPIE’s 48th Annual Meeting tenutosi a San Diego, USA nel 3-8 August, 2003) [10.1117/12.513900].
Time-frequency characterization of random systems
GALLEANI, Lorenzo;
2003
Abstract
We have previously presented a method to write equations for the Wigner distribution corresponding to the solution of a linear differential equation. We extend this method to arbitrary time-frequency distributions, the Short Time Fourier Transform, and the wavelet transform. Also, we apply the method to stochastic signals and address a number of applications including Brownian motion. We obtain the Wigner distribution for Brownian motion by solving the Langevin equation and also by using our method. We obtain exact solutions.
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https://hdl.handle.net/11583/1663165
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