Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carr...Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature 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 modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.展开更多
基金supported by the National Key R&D Program of China(Grant Nos.2019YFA0709600,2019YFA0709602)by the Beijing Natural Science Foundation(Grant No.Z220003).
文摘Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature 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 modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.
