Injection-locked oscillators are shown to act as narrow-band tunable filters for FM signals if the modulation rate is much larger than the locking bandwidth. The filtering action of the injection-locked oscillator for FM signals is found analogous to that of a high Q passive cavity. The effective Q of the injection-locked oscillator can be as high as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> if the stability of the injected signal carrier and oscillator frequencies is better than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> . These filtering properties can be applied to a digital demodulator for coherent phase detection of a coded FM signal. The local source which is required for coherent phase detection is provided by using a fraction of the received signal to lock an oscillator. Sideband suppression and carrier amplification of the injected signal are achieved simultaneously by using the filtering action of the injection-locked oscillator. The simplicity of this digital demodulator makes it appear useful for repeaters in microwave radio relays.