The evolution equations in study of the cavity oscillations excited by a digital signal

The problem of electromagnetic oscillations in a cavity excited by a signal of finite duration is considered. The singly connected cavity surface has arbitrary geometrical form and it is perfectly conducting physically; its volume is filled with a homogeneous lossy medium. The formulation of the problem involves the principle of causality. The problem is solved within the frames of the evolutionary approach to electromagnetics. The electromagnetic field is presented as an eigenmodal expansion with time dependent modal amplitudes. The amplitudes satisfy a system of evolution (i.e., with time derivative) ordinary differential equations, which are derived and studied. Explicit solutions are obtained satisfying the principle of causality automatically. Numerical examples for the cavity oscillations excited by the Walsh function signals are exhibited, some resonances of the digital signals are revealed.