The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters

William Kenneth Jenkins, Benjamin J. Leon

    Research output: Contribution to journalArticle

    161 Citations (Scopus)

    Abstract

    A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.

    Original languageEnglish (US)
    Pages (from-to)191-201
    Number of pages11
    JournalIEEE Transactions on Circuits and Systems
    Volume24
    Issue number4
    DOIs
    StatePublished - Jan 1 1977

    Fingerprint

    Numbering systems
    FIR filters
    Digital filters
    Hardware
    Bandpass filters
    Impulse response
    Decoding

    All Science Journal Classification (ASJC) codes

    • Engineering(all)

    Cite this

    Jenkins, William Kenneth ; Leon, Benjamin J. / The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters. In: IEEE Transactions on Circuits and Systems. 1977 ; Vol. 24, No. 4. pp. 191-201.
    @article{db15a8f885fd48df9846e3c0ce7b34ae,
    title = "The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters",
    abstract = "A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.",
    author = "Jenkins, {William Kenneth} and Leon, {Benjamin J.}",
    year = "1977",
    month = "1",
    day = "1",
    doi = "10.1109/TCS.1977.1084321",
    language = "English (US)",
    volume = "24",
    pages = "191--201",
    journal = "IEEE Transactions on Circuits and Systems",
    issn = "0098-4094",
    publisher = "Institute of Electrical and Electronics Engineers Inc.",
    number = "4",

    }

    The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters. / Jenkins, William Kenneth; Leon, Benjamin J.

    In: IEEE Transactions on Circuits and Systems, Vol. 24, No. 4, 01.01.1977, p. 191-201.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters

    AU - Jenkins, William Kenneth

    AU - Leon, Benjamin J.

    PY - 1977/1/1

    Y1 - 1977/1/1

    N2 - A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.

    AB - A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.

    UR - http://www.scopus.com/inward/record.url?scp=0017481467&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0017481467&partnerID=8YFLogxK

    U2 - 10.1109/TCS.1977.1084321

    DO - 10.1109/TCS.1977.1084321

    M3 - Article

    VL - 24

    SP - 191

    EP - 201

    JO - IEEE Transactions on Circuits and Systems

    JF - IEEE Transactions on Circuits and Systems

    SN - 0098-4094

    IS - 4

    ER -