A supersonic compressor rotor that includes a rotor disk that includes a substantially cylindrical endwall, a radially inner surface, and a radially outer surface. The endwall extends between the radially inner surface and the radially outer surface. A plurality of vanes are coupled to the endwall. The vanes extend outwardly from the endwall. Adjacent vanes form a pair and are spaced a circumferential distance apart such that a flow channel is defined between each pair of circumferentially-adjacent vanes. The flow channel extends generally radially between an inlet opening and an outlet opening. A first supersonic compression ramp is coupled to the endwall. The first supersonic compression ramp is positioned within the flow channel to facilitate forming at least one compression wave within the flow channel.