Techniques for Computing the Discrete Fourier Transform Using the Quadratic Residue Fermat Number Systems

Truong,; Chang,; Hsü,; Pei, Pei; Reed,

doi:10.1109/tc.1986.1676704

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…In the next section we shall give a necessary and sufficient condition for the existence of sum of two copies of Z M of M 2 elements.This theorem is a special case of lemma 2.3, proved by Cozzens and Finkelstein in [3]. A similar result for the case of Gaussian integers is proposed in[9].…”

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confidence: 65%

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A residue number system implementation of real orthogonal transforms

Dimitrov

Jullien

Miller

1998

IEEE Trans. Signal Process.

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Recent work has focused on performing residue computations that are quantized within a dense ring of integers in the real domain. The aims of this paper are to provide an efficient algorithm for the approximation of real input signals, with arbitrarily small error, as elements of a quadratic number ring, and to prove RNS moduli restrictions for simplified multiplication within the ring. The new approximation scheme can be used for implementation of real-valued transforms and their multidimensional generalizations.

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confidence: 65%

“…Let us consider the approximation of the number x =0.8036. The representation of x in the -irrational number system with 20 digits precision is: (9) After substituting the corresponding powers we have: (10) We should mention that in the -irrational number system, the minimal distance between ones is 3, that is, combinations of digits.…”

Section: Some Examplesmentioning

confidence: 99%

A residue number system implementation of real orthogonal transforms

Dimitrov

Jullien

Miller

1998

IEEE Trans. Signal Process.

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“…Therefore, the design of efficient modulo 2 n +1 adders is critical [15] . Modulo 2 n +1 operations are used in many applications such as DSP algorithms [16] , Fermat Number Transform for elimination of round off errors in convolution computations [17,18,19] , cryptography [20] and in pseudorandom number generation [21] . Modulo 2 n + 1 adders are also utilized as the last stage adder of modulo 2 n +1 multipliers.…”

Section: 221mentioning

confidence: 99%

Low Power Modulo 2n+1 Adder Based on Carry Save Diminished-One Number System

Timarchi¹,

Kavehei²,

Navi³

2008

American J. of Applied Sciences

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Modulo 2 n +1 adders find great applicability in several applications including RNS implementations. This paper presents a new number system called Carry Save Diminished-one for modulo 2 n +1 addition and a novel addition algorithm for its operands. In this paper, we also present a novel architectures for designing modulo 2 n +1 adders, based on parallel-prefix carry computation units. CMOS implementations reveal the superiority of the resulting adders against previously reported solutions in terms of implementation area and delay.

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