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.