Asymptotic Theory for the Circuit Envelope Analysis (Journal of Computational Mathematics, 2024)
Asymptotic theory for the circuit envelope analysis is developed in this paper. A typicalfeature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave, and the other is the slow timescale of modulationsignal. We first perform pro forma asymptotic analysis for both the driven and autonomoussystems. Then resorting to the Floquet theory of periodic operators, we make a rigorousjustification for first-order asymptotic approximations. It turns out that these asymptoticresults are valid at least on the slow timescale. To speed up the computation of asymptoticapproximations, we propose a periodization technique, which renders the possibility ofutilizing the NUFFT algorithm. Numerical experiments are presented, and the resultsvalidate the theoretical findings.