Time and Frequency Domain Specifications for Continuous Signals.

Aleksandar Chakarov (Univ. Colorado, Boulder)

Joint work with Sriram Sankaranarayanan (Univ. Colorado, Boulder) and Georgios Fainekos (Arizona State University, Tempe, Az).

We present a methodology for specifying periodic signals using time domain as well as frequency domain 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. Specifically, the constraints bound the maximum possible amplitude at a given frequency. The combination of time and frequency domain specifications yields mixed-domain specifications that constrain a signal to belong to the intersection of the time and frequency domain specifications.

In this talk, we present our specification formalisms and some key results on the signal recognition and the signal generation problems.