Residue number system implementations of complex heterodyne tunable filters

The heterodyne signals for a complex heterodyne filter based upon M/2 equally-spaced heterodyne frequencies between DC and the Nyquist frequency can be generated from taking integer powers of the M^th root of one. In residue number systems (RNS) based on prime moduli of the form Mk+1, where k is an integer, the Mth root of one and its powers can be represented by integer values within the RNS. These M^th-root residue number systems (MRNS) are ideal for implementing complex heterodyne filters that allow for the tuning of digital filters between DC and the Nyquist frequency. Using MRNS exact arithmetic can be carried out on these complex signals with errors only occurring at the output when MRNS is converted to binary. The result is a tunable linear-phase filter that is convenient to implement and uses less hardware than conventional tunable filters.