Title :
Response of Dynamical Systems to Nonstationary Inputs
Author :
Galleani, Lorenzo
Author_Institution :
Politec. di Torino, Torino, Italy
Abstract :
We obtain the time-frequency response of the output of a dynamical system when the input belongs to a class of common nonstationary signals, namely, an impulse, a linear chirp, a causal sinusoid, and a short duration sinusoid. The obtained results clarify how the system processes the time-varying frequencies of the input signal to generate the time-frequency spectrum of the output. All analytic results are exact. The solution is obtained by developing a method which can be used to evaluate the output of a dynamical system for complex combinations of nonstationary inputs. We show numerical examples which prove that the response of a system to a nonstationary input is made by a series of events occurring in the joint time-frequency domain.
Keywords :
dynamic response; frequency response; signal processing; time-frequency analysis; causal sinusoid; dynamical system response; joint time-frequency domain; linear chirp; nonstationary input signal; short duration sinusoid; time-frequency response; time-frequency spectrum; time-varying frequency; Approximation methods; Biological system modeling; Differential equations; Interference; Mathematical model; Smoothing methods; Time frequency analysis; Differential equations; Wigner distribution; dynamical systems; nonstationary signals; time-frequency analysis;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2214032