Direct Time-Frequency Characterization of Linear Systems Governed by Differential Equations

We present a new method to study linear systems that exhibit time-varying characteristics and are governed by ordinary differential equations. The method transforms the differential equation into the governing equation for the ambiguity function and to the time-frequency domain. The advantage of the method is that in the new domain an immense simplification occurs, both mathematically and physically. The method applies to both deterministic and stochastic differential equations. The approach is applied to the classical RC filter driven by white noise. We obtain a new characterization of the output spectra.