Multiple-input multiple-output (MIMO) random systems are a common model for stochastic phenomena. These systems can be transformed to the time-frequency domain to gain a much deeper insight in the behavior of the solution (the output signal) when the forcing term (the input signal) is a nonstationary random process. For this fundamental physical case, in fact, the frequency content of both the input and the output signals changes with time, and it can be represented in an effective way by using time-frequency analysis. The result of the transformation is a time-frequency system. In this article we show how an initial value problem in the time domain can be transformed to the time-frequency domain. We prove that the initial conditions can be incorporated in the input of the time-frequency system. We apply our method to the case of a MIMO system with two vibrational modes.
Time-frequency initial value problems for Random MIMO systems / Galleani, Lorenzo (OPERATOR THEORY). - In: Pseudo-Differential Operators and Generalized Functions / Pilipović S., Toft J.. - STAMPA. - Basel : Springer International Publishing, 2015. - ISBN 978-3-319-14617-1. - pp. 67-78 [10.1007/978-3-319-14618-8_6]
Time-frequency initial value problems for Random MIMO systems
GALLEANI, Lorenzo
2015
Abstract
Multiple-input multiple-output (MIMO) random systems are a common model for stochastic phenomena. These systems can be transformed to the time-frequency domain to gain a much deeper insight in the behavior of the solution (the output signal) when the forcing term (the input signal) is a nonstationary random process. For this fundamental physical case, in fact, the frequency content of both the input and the output signals changes with time, and it can be represented in an effective way by using time-frequency analysis. The result of the transformation is a time-frequency system. In this article we show how an initial value problem in the time domain can be transformed to the time-frequency domain. We prove that the initial conditions can be incorporated in the input of the time-frequency system. We apply our method to the case of a MIMO system with two vibrational modes.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2643101
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