Whenever the Doppler effect is mentioned, it's typically in the context of sound waves or electromagnetic radiation. On the cosmological scale, red-shifting is also important because of the enormous speed of receding galaxies, thanks to the expansion of the universe.
Yet, red-shift is always discussed as the red-shifting of electromagnetic waves. Can gravitational waves be red-shifted? If so, could observations of them be used like red-shifted electromagnetic waves from distant sources are; that is, to figure out how fast an object is receding?