Title :
A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 22n+ 1
Author :
Shyu, H.C. ; Truong, T.K. ; Reed, I.S.
Author_Institution :
Department of Electrical Engineering, University of Southern California
Abstract :
A quadratic-polynomial Fermat residue number system (QFNS) can be used to compute the complex multiplications needed to perform a DFT. The advantage of such a QFNS is that complex multiplication can be accomplished with only two integer multiplications. In this paper, it is shown that a new set of numbers of the form Tn = 22n + 1 can be used in place of the set of Fermat numbers. This new quadratic residue number system can be used also to compute a complex multiplication with only two integer multiplications.
Keywords :
Chinese Remainder Theorem; VLSI; direct sum; dynamic range; modulo; quadratic-polynomial residue number system; Arithmetic; Computer architecture; Discrete Fourier transforms; Dynamic range; Fast Fourier transforms; Fourier transforms; Laboratories; NASA; Propulsion; Very large scale integration; Chinese Remainder Theorem; VLSI; direct sum; dynamic range; modulo; quadratic-polynomial residue number system;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.1987.1676868
