These compression devices like Comprex that use phased ports and ducts in a rotating drum to utilize dynamic exhaust gas pressure waves to compress an intake air charge, look very attractive on paper due to their high efficiency, good throttle response, and high speed capability.
If you look at the paper linked by RodRico, the most attractive use of the device is as a HP compressor stage in a turbine engine, due to its capability to operate at relatively high speed, handle high air flows, give a high PR from its stage at good efficiency, and add minimal weight. In reality, there are very difficult problems to resolve, such as sealing of the rotor end faces. If someone can figure out a reliable method to solve these problems, this device could have a big market for use in turbine engines as a way to significantly increase PR, and thus improve TE/SFC.