Mixed Frequency-Time Method

  • Kenneth S. Kundert
  • Jacob K. White
  • Alberto Sangiovanni-Vincentelli
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 94)


In this chapter a boundary constraint is developed that restricts the set of solutions of a differential equation to those that are quasiperiodic. A first attempt is made by using the periodic boundary constraint (3.21 c), but it is shown to be computationally too expensive. In the process it is discovered that there are periodic problems that are better handled with a quasiperiodic boundary constraint. Another approach was suggested by Chua and Ushida [chua81]. They construct an Appoint quasiperiodic boundary constraint by, assuming that the quasi-periodic signals are accurately approximated by a Fourier series with just K frequencies ΛK = {0, ω1, . . . , ω K-1}, sampling the waveforms at M > 2K - 1 points τ = {t 1, t 2,. . . , t M}, and insisting that the resulting sampled waveform is quasiperiodic (i.e., it belongs to AP K , τ)). This method trades off accuracy for efficiency, but the tradeoff is such that the method is impractical for almost all problems. A generalization of this approach, referred to as the mixed frequency-time method (MFT), avoids both the efficiency and accuracy problems of the previous methods and is discussed in much greater depth.


Fourier Series Clock Cycle Fourier Coefficient Input Frequency Boundary Constraint 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth S. Kundert
    • 1
  • Jacob K. White
    • 2
  • Alberto Sangiovanni-Vincentelli
    • 3
  1. 1.Cadence Design SystemsUSA
  2. 2.Massachusetts Institute of TechnologyUSA
  3. 3.University of CaliforniaBerkeleyUSA

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