Block diagram reduction of the interconnected linear time-varying systems in the time-frequency domain

The problem of obtaining the time-frequency domain input-output model of a linear time-varying (LTV) system formed by linking the time-frequency domain blocks describing LTV subsystems is considered. Simultaneous input-output transformation of the constituent LTV subsystems modeled in terms of two-dimensional impulse responses into time-frequency domain is developed. It is shown that this transformation gives rise to the time-frequency domain subsystem representation which lends itself easily to: 1) deriving composition rules for obtaining the simplified overall interconnection model, and 2) revealing the constraints on individual subsystem modeling that need to be satisfied to admit such simplification. These composition rules are developed for the reduction of standard topologies including series, parallel, and feedback interconnections. The reduction of a more complicated topology using these rules is demonstrated.