(image found at:  Google)
I can only imagine they named this device the comprex because it is exactly that, extremely comprex, err... complex.

A friend sent me a link to a device called a comprex. This device is a third option in the world of f/i, its not a turbo and not a supercharger but better than both. From what I read and understood this device uses shock waves to compress air.
When I first saw the comprex it reminded me of a wheel you see on the back of the old ships, (water wheel?) enclosed in a casing. Essentially there are openings or ports on both sides of the casing which allow air and exhaust to enter the spaces between the fins respectively, much like a turbo.  Air enters a port on the left side and the wheel spins closing off both the exhaust port and the intake port. The wheel rotates a little more allowing exhaust gases to enter from the right side at a high pressure and creates a shock wave pushing the fresh air against the left side of the casing, compressing it.  The right side of the port opens.  This port is sized smaller and the air must leave at a slower velocity than it wants to; creating a second shock wave back towards the right side of the wheel pushing the air against a closed port further compressing it. The compressed air is reflected off the port back to the left side of the wheel pushing the compressed air out.
 
Notes:
The exhaust and air never mix because the shock wave travels to fast; (at the speed of sound)
Since the waves travel at the speed of sound you eliminate turbo lag and response is instant.
You do have a pulley connected to the comprex wheel so it can spin but the pulley does not suck noticeable power form the engine.