A pulsejet is an engine with a few moving parts (only the chamber shutters I think) in which fuel is injected in the combustion chamber, leading to a explosion that pushes air to the exhaust. After the explosion, the air flows to the chamber again, leading to a new explosion and the cycle continues.
This type of engine is really inefficient for a number of reasons, but to me this kinda resembles a piston engine; in the sense that it also works by small explosions. Unlike the pulsejet, the piston engines compresses air (the second stage of the combustion cycle on the picture).
From what I could find, in normal turbine engines (like turbofan, turbojet, turboshaft, etc.) the combustion chamber works by a continuous flow of extremely compressed air that continuously expands towards the back, spinning the turbine and continuing the cycle.
Also, I suppose you wouldn't like it to run as fast as a conventional pulsejet (because I've read that the Pulsejets used in the WW2 couldn't last more than a single flight), I would think of small compressor, like a turbocharger, but moved by the turbine (or something like that) in small pulses. But again, I'm only making assumptions.
I tried to search for any kind of research about it, but I could only find this weird turbo-fan concept from a Kiberius Aircraft PDF with the title of "PULSE DETONATION ENGINE TECHNOLOGY: AN OVERVIEW" (the link immediatly downloads the PDF file).
So, in the document says that in the bypass air zone (in the image, page 18) there would be an extra combustion chamber in which would speed up air even more through pulses. But this sounds more like a turbofan-pulsejet modification rather than a pulsejet with a turbine at its end.