A supersonic compressor rotor comprising: a rotor disk comprising a substantially cylindrical endwall, a radially inner surface, and a radially outer surface, said cylindrical endwall extending between said radially inner surface and said radially outer surface; a plurality of vanes coupled to said cylindrical endwall, said vanes extending outwardly from said cylindrical endwall, adjacent vanes forming a pair and are spaced a circumferential distance apart such that a flow channel is defined between each said pair of circumferentially-adjacent vanes, said flow channel extending generally radially between an inlet opening and an outlet opening characterized in that: a first supersonic compression ramp coupled to said endwall, said first supersonic compression ramp positioned within said flow channel to facilitate forming at least one compression wave within said flow channel; a shroud assembly coupled to said vanes, said vanes extending between an inner surface of said shroud assembly and said endwall; and a second supersonic compression ramp coupled to said inner surface, said second compression ramp extending from said inner surface towards said endwall; wherein said second supersonic compression ramp is positioned with respect to said first supersonic compression ramp such that said throat region of said flow channel is defined between said first supersonic compression ramp and said second supersonic compression ramp. a rotor disk comprising a substantially cylindrical endwall, a radially inner surface, and a radially outer surface, said cylindrical endwall extending between said radially inner surface and said radially outer surface; a plurality of vanes coupled to said cylindrical endwall, said vanes extending outwardly from said cylindrical endwall, adjacent vanes forming a pair and are spaced a circumferential distance apart such that a flow channel is defined between each said pair of circumferentially-adjacent vanes, said flow channel extending generally radially between an inlet opening and an outlet opening characterized in that: a first supersonic compression ramp coupled to said endwall, said first supersonic compression ramp positioned within said flow channel to facilitate forming at least one compression wave within said flow channel; a shroud assembly coupled to said vanes, said vanes extending between an inner surface of said shroud assembly and said endwall; and a second supersonic compression ramp coupled to said inner surface, said second compression ramp extending from said inner surface towards said endwall; wherein said second supersonic compression ramp is positioned with respect to said first supersonic compression ramp such that said throat region of said flow channel is defined between said first supersonic compression ramp and said second supersonic compression ramp. a first supersonic compression ramp coupled to said endwall, said first supersonic compression ramp positioned within said flow channel to facilitate forming at least one compression wave within said flow channel; a shroud assembly coupled to said vanes, said vanes extending between an inner surface of said shroud assembly and said endwall; and a second supersonic compression ramp coupled to said inner surface, said second compression ramp extending from said inner surface towards said endwall; wherein said second supersonic compression ramp is positioned with respect to said first supersonic compression ramp such that said throat region of said flow channel is defined between said first supersonic compression ramp and said second supersonic compression ramp.