phase and frequency variations

If a star has a (relatively) coherent oscillation mode, and you can monitor it over a long period of time, then orbital motion of the star can be seen as either phase or frequency variations of that mode. I've been working on this in different collaborations, with Dan Hey, with Simon J Murphy, with Abby Shaum (CUNY), and recently with Nora Eisner (Flatiron). Right now, Shaum, Eisner, and I are looking at signal-processing approaches that look like demodulators. What I'm interested in—at least in terms of me learning about signal processing—is how can we make a demodulator that demodulates both phase and frequency simultaneously. There must be hybrid and combined approaches. I'm also interested in what we can measure from incoherent oscillators.