Simon J Murphy (Sydney) has made some great discoveries of binary companions to delta-Scuti stars by looking at asteroseismic mode phase shifts: As the star orbits the system barycenter, the time-of-flight from star to Earth is modulated by the binary orbit. That appears as time delays in the asteroseismic oscillation mode phase. He can analyze each mode individually and see the same orbital distortion to every mode.
Now think of the asteroseismic mode as a carrier frequency. Then the orbit is modulating the frequency of the mode. Murphy phrases things in terms of time delays (light-crossing time) but it can also be phrased in terms of redshift and blueshift of the mode. The light-travel time is just an integral of the Doppler shift. That Doppler shift modulates the frequency.
So these stars are like FM radios with carrier frequencies at the asteroseismic mode frequencies, and the signal (the song they are playing) encoded as a continuous frequency shift. So let's apply the various methods for FM-radio demodulation to these signals and see the companions! This project is super straightforward: Get Kepler data; code up demodulator; run; plot.
