A method and system is disclosed for designing a radio for down-converting RF signals to IF signals by sampling the signals in a round-robin sampling circuit and multiplying the samples by coefficients that are changed at a fixed rate equal to the rate of operation of each of the sampling circuits. The circuit is able to down-convert multiple channels simultaneously to adjacent positions in the IF band, while rejecting unwanted image signals. The method and system avoids the difficulty and cost of directly digitizing the RF signal, allowing each component to operate at a greatly reduced speed. The coefficients are selected to provide the desired transfer function while keeping the output signal centered at a desired frequency.