Archivio Istituzionale della RicercaWe derive a simple relationship between the Wigner distribution of the Green’s function of the Langevin equation and of the harmonic oscillator. This relationship shows that the Wigner distribution of the Green’s function of the harmonic oscillator consists of the sum of two terms obtained by translating the Wigner distribution of the Green’s function of the Langevin equation at the resonant frequencies of the harmonic oscillator, plus an interference term. This result paves the way for a simplification of the time-frequency representation of differential equations, as well as for a better understanding and filtering of interference terms.
A time-frequency relationship between the Langevin equation and the harmonic oscillator / Galleani, Lorenzo (TRENDS IN MATHEMATICS). - In: Pseudo-Differential Operators: Groups, Geometry and ApplicationsSTAMPA. - Basel : Springer International Publishing, 2017. - ISBN 978-3-319-47511-0. - pp. 119-131 [10.1007/978-3-319-47512-7_6]
A time-frequency relationship between the Langevin equation and the harmonic oscillator
Galleani, Lorenzo
2017
Abstract
We derive a simple relationship between the Wigner distribution of the Green’s function of the Langevin equation and of the harmonic oscillator. This relationship shows that the Wigner distribution of the Green’s function of the harmonic oscillator consists of the sum of two terms obtained by translating the Wigner distribution of the Green’s function of the Langevin equation at the resonant frequencies of the harmonic oscillator, plus an interference term. This result paves the way for a simplification of the time-frequency representation of differential equations, as well as for a better understanding and filtering of interference terms.
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https://hdl.handle.net/11583/2693289
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