An efficient apparatus for performing frequency conversion from a final IF frequency to a baseband frequency is described. A counter (401) generates two logical signals G1 (402) and G2 (403) which are passed to an exclusive-OR gate (404) and a multiplexer (406). When a control signal (411) is deasserted, multiplexer (406) passes signal G1 to I1 and signal G2 to I2; when control signal (411) is asserted, multiplexer (406) passes binary signal G1 to I2 (410) and signal G2 to I1 (407). Similarly, multiplexer (405) swaps its input real and imaginary samples when the output of exclusive-OR gate (404) is asserted; otherwise, it performs no operation on its input samples. Signals I1 (407) and I2 (410) are used to control arithmetic inverters (408) and (409) respectively. When the controlling signal for either inverter is asserted, the inventer performs arithmetic inversion, otherwise it performs no operation.