• DocumentCode
    1078578
  • Title

    Generalized Fermat-Mersenne number theoretic transform

  • Author

    Dimitrov, Vassil S. ; Cooklev, Todor V. ; Donevsky, Borislav D.

  • Author_Institution
    Plovdiv Univ., Bulgaria
  • Volume
    41
  • Issue
    2
  • fYear
    1994
  • fDate
    2/1/1994 12:00:00 AM
  • Firstpage
    133
  • Lastpage
    139
  • Abstract
    A generalization of the Fermat and Mersenne number transform is suggested. The transforms are defined over finite fields and rings. This paper establishes the conditions necessary for these numbers to be prime. The length of the transforms is a highly composite number. An algorithm for finding primitive roots of unity is also discussed. The proposed transforms are characterized by respectable combinations of transform length, dynamic range and computational efficiency and can be used for fast convolution of integer sequences
  • Keywords
    number theory; signal processing; transforms; Fermat-Mersenne number theoretic transform; computational efficiency; dynamic range; fast convolution; finite fields; finite rings; integer sequences; number theoretic transform; prime numbers; primitive roots; transform length; Arithmetic; Computational efficiency; Convolution; Decoding; Digital filters; Dynamic range; Fast Fourier transforms; Filtering; Galois fields; Image processing;
  • fLanguage
    English
  • Journal_Title
    Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    1057-7130
  • Type

    jour

  • DOI
    10.1109/82.281844
  • Filename
    281844
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1078578