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This paper reviews some of the promising doors that functional analysis techniques have recently opened in the field of electronic circuit simulation. Because of the modulated nature of radio frequency (RF) signals, the corresponding electronic circuits seem to operate in a slow time scale for the aperiodic information and another, much faster, time scale for the periodic carrier. This apparent multirate behavior can be appropriately described using partial differential equations (PDEs) within a bivariate framework, which can be solved in an efficient way using hybrid time-frequency techniques. With these techniques, the aperiodic information dimension is treated in the discrete time domain, while the periodic carrier dimension is processed in the frequency domain, in which the solution is evaluated within a space of harmonically related sinusoidal functions. The objective of this paper is thus to provide a general overview on the most important hybrid time-frequency techniques, as the ones found in commercial tools or the ones recently published in the literature.

Recent Developments on Hybrid Time-Frequency Numerical Simulation Techniques for RF and Microwave Applications