Is it possible to combine airbreathing ramjet engines with pulejets?

It would be basically be a daul-cycle engine that would potentially allow for self-launching hypersonic ramjet powered aircraft.

Ramjets, by design, cannot function at zero airspeed. However, a pulsejet launch cycle could provide the initial thrust to accelerate the aircraft on the runway from a standstill, until it is moving fast enough for the more-efficient ramjet cycle to take over, and the pulsejet is switched off. This would eliminate the need for the aircraft to be launched as a parasite from a large mothership, making it infinitely more versatile.

The trickiest part would be integrating the pulsejet housing and the ramjet housing into the same nacelle, where the air inlet for the pulsejet can be closed off at high speeds, and possibly re-opened for a landing approach. Ase pulsejets have very poor specific impulse, it would be best to only use that cycle during take off and acceleration. The pulsejet however would be far cheaper and simpler to integrate into a ramjet housing than a conventional turbojet or turbofan.

Thoughts? Would this actually be worth investigating?