Title :
Generalized Fermat-Mersenne number theoretic transform
Author :
Dimitrov, Vassil S. ; Cooklev, Todor V. ; Donevsky, Borislav D.
Author_Institution :
Plovdiv Univ., Bulgaria
fDate :
2/1/1994 12:00:00 AM
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;
Journal_Title :
Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on
