Transient analysis of random systems

Lorenzo Galleani

doi:10.1117/12.725635

21 June 2007 Transient analysis of random systems

Lorenzo Galleani

Proceedings Volume 6603, Noise and Fluctuations in Photonics, Quantum Optics, and Communications; 66030M (2007) https://doi.org/10.1117/12.725635
Event: SPIE Fourth International Symposium on Fluctuations and Noise, 2007, Florence, Italy

Abstract

We define the transient spectrum as the time-frequency spectrum of a random system undergoing a transient behavior. We show that the transient spectrum approaches the classical frequency spectrum when time goes to infinity. We prove that it is always possible to decompose the transient spectrum into the sum of a stationary spectrum and a decaying spectrum. The stationary spectrum is, up to a constant, the classical power spectrum, while the decaying spectrum accounts for the nonstationary behavior of the transient. All the results are valid for random LTI systems defined by stochastic differential equations of n-th order. The Langevin equation is studied as an example.

Citation Download Citation

Lorenzo Galleani "Transient analysis of random systems", Proc. SPIE 6603, Noise and Fluctuations in Photonics, Quantum Optics, and Communications, 66030M (21 June 2007); https://doi.org/10.1117/12.725635

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