A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2&lt;sup&gt;2n&lt;/sup&gt;+ 1

H.C. Shyu; T.K. Truong; I.S. Reed

doi:10.1109/TC.1987.1676868

Publication
1987
Issue No. 10 - October
Abstract - A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2<sup>2n</sup>+ 1

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A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2²ⁿ+ 1

October 1987 (vol. 36 no. 10)

pp. 1255-1258

	ASCII Text	x
	H.C. Shyu, T.K. Truong, I.S. Reed, "A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2<sup>2n</sup>+ 1," IEEE Transactions on Computers, vol. 36, no. 10, pp. 1255-1258, October, 1987.

	BibTex	x
	@article{ 10.1109/TC.1987.1676868, author = {H.C. Shyu and T.K. Truong and I.S. Reed}, title = {A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2<sup>2n</sup>+ 1}, journal ={IEEE Transactions on Computers}, volume = {36}, number = {10}, issn = {0018-9340}, year = {1987}, pages = {1255-1258}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1987.1676868}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - JOUR JO - IEEE Transactions on Computers TI - A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2<sup>2n</sup>+ 1 IS - 10 SN - 0018-9340 SP1255 EP1258 EPD - 1255-1258 A1 - H.C. Shyu, A1 - T.K. Truong, A1 - I.S. Reed, PY - 1987 KW - VLSI KW - Chinese Remainder Theorem KW - direct sum KW - dynamic range KW - modulo KW - quadratic-polynomial residue number system VL - 36 JA - IEEE Transactions on Computers ER -

H.C. Shyu, Department of Electrical Engineering, University of Southern California

T.K. Truong

I.S. Reed

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.1987.1676868

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.

Index Terms:

VLSI, Chinese Remainder Theorem, direct sum, dynamic range, modulo, quadratic-polynomial residue number system

Citation:

H.C. Shyu, T.K. Truong, I.S. Reed, "A Complex Integer Multiplier Using the Quadratic-Polynomial Residue Number System with Numbers of Form 2²ⁿ+ 1," IEEE Transactions on Computers, vol. 36, no. 10, pp. 1255-1258, Oct. 1987, doi:10.1109/TC.1987.1676868

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