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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 578326, 11 pages
Review Article

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

1School of Technology and Management, Polytechnic Institute of Leiria, Morro do Lena, Alto Vieiro, Apartado 4163, 2411-901 Leiria, Portugal
2Institute of Telecommunications, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal

Received 11 October 2012; Accepted 11 December 2012

Academic Editor: Davide La Torre

Copyright © 2013 Jorge F. Oliveira and José C. Pedro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.