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Traditional digital heterodyne circuits store samples of a quarter cosine wave in a look-up-table (LUT) and utilize digital multiplier hardware to multiply samples of the cosine times the input samples to the heterodyne unit resulting in an output that is the product of the input signal and the cosine wave. However, by storing the canonic-sign-digit (CSD) shift and add sequences in the LUT, rather than the samples of the cosine, it is possible to implement the entire digital heterodyne circuit with only two adder/subtractor units and three switches. The new circuit represents a considerable savings in hardware yet provides identical performance when compared to the traditional digital heterodyne circuit. Such circuits are very important in modern communications systems where they provide up-conversion, down-conversion, FSK and PSK modulation and other critical functions associated with digital communications systems and software radios.