Time-Frequency Representation of MIMO Dynamical Systems

Many deterministic and random physical signals can be modeled as the output of a multi-input-multi-output (MIMO) dynamical system. Since physical signals are typically nonstationary, their frequency content changes with time. To understand this time variation, we transform the MIMO system to the time-frequency domain. The result is a time-frequency MIMO dynamical system, whose input and output are the time-frequency spectra of the original input and output signals in the time domain. The time-frequency system reveals the spectral mechanisms involved in the generation of nonstationary signals. We apply our method to the case of a MIMO system with two vibrational modes and a nonstationary noise at the input. We obtain the time-frequency spectrum of the output, which shows how the spectrum of the modes changes with time. This result cannot be achieved with classical spectral techniques, because they require the input random process to be wide sense stationary.