The Design of Dual-Mode Complex Signal Processors Based on Quadratic Modular Number Codes

W. K. Jenkins, J. V. Krogmeier

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations


    It has been known for a long time that quadratic modular number codes admit an unusual representation of complex numbers which leads to complete decoupling of the real and imaginary channels, thereby simplifying complex multiplication and providing error isolation between the real and imaginary channels. This paper first presents a tutorial review of the theory behind the different types of complex modular rings (fields) that result from particular parameter selections, and then presents a theory for a “dual-mode” complex signal processor based on the choice of augmented power-of-2 moduli. It is shown how a diminished-1 binary code, used by previous designers for the realization of Fermat number transforms, also leads to efficient realizations for dual-mode complex arithmetic for certain augmented power-of-2 moduli. Then a design is presented for a recursive complex filter based on a ROM/ACCUMULATOR architecture and realized in an augmented power-of-2 quadratic code, and a computer-generated example of a complex recursive filter is shown to illustrate the principles of the theory.

    Original languageEnglish (US)
    Pages (from-to)354-364
    Number of pages11
    JournalIEEE Transactions on Circuits and Systems
    Issue number4
    StatePublished - Apr 1987

    All Science Journal Classification (ASJC) codes

    • Engineering(all)


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