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Combining Time and Frequency Domain Specifications for Periodic Signals

  • Aleksandar Chakarov
  • Sriram Sankaranarayanan
  • Georgios Fainekos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7186)

Abstract

In this paper, we investigate formalisms for specifying periodic signals using time and frequency domain specifications along with algorithms for the signal recognition and generation problems for such specifications. The time domain specifications are in the form of hybrid automata whose continuous state variables generate the desired signals. The frequency domain specifications take the form of an “envelope” that constrains the possible power spectra of the periodic signals with a given frequency cutoff. The combination of time and frequency domain specifications yields mixed-domain specifications that constrain a signal to belong to the intersection of the both specifications.

We show that the signal recognition problem for periodic signals specified by hybrid automata is NP-complete, while the corresponding problem for frequency domain specifications can be approximated to any desired degree by linear programs, which can be solved in polynomial time. The signal generation problem for time and frequency domain specifications can be encoded into linear arithmetic constraints that can be solved using existing SMT solvers. We present some preliminary results based on an implementation that uses the SMT solver Z3 to tackle the signal generation problems.

Keywords

Frequency Domain Temporal Logic Periodic Signal Signal Recognition Hybrid Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aleksandar Chakarov
    • 1
  • Sriram Sankaranarayanan
    • 1
  • Georgios Fainekos
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.Arizona State UniversityTempeUSA

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