Combining time and frequency domain specifications for periodic signals

Aleksandar Chakarov, Sriram Sankaranarayanan, Georgios Fainekos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationRuntime Verification - Second International Conference, RV 2011, Revised Selected Papers
Pages294-309
Number of pages16
DOIs
StatePublished - May 23 2012
Event2nd International Conference on Runtime Verification, RV 2011 - San Francisco, CA, United States
Duration: Sep 27 2011Sep 30 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7186 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Conference on Runtime Verification, RV 2011
CountryUnited States
CitySan Francisco, CA
Period9/27/119/30/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Chakarov, A., Sankaranarayanan, S., & Fainekos, G. (2012). Combining time and frequency domain specifications for periodic signals. In Runtime Verification - Second International Conference, RV 2011, Revised Selected Papers (pp. 294-309). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7186 LNCS). https://doi.org/10.1007/978-3-642-29860-8_22