Results 241 to 250 of about 9,400,159 (276)

Number theoretic transform based on ternary arithmetic

ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005
A number theoretic transform (NTT) is proposed, which can efficiently be computed by using ternary modular arithmetic. The new NTT relaxes the restriction imposed on the convolution length and, as in other efficient NTT's, its computation can be performed by means of data shifts and additions.
Prabhakara C. Balla, Andreas Antoniou
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Number Theoretic Transforms

1977
The theory of Number Theoretic Transforms having circular convolution properties is developed from the definition of circular convolution. The application of these transforms to digital signal processing is discussed. The lectures include the following sections. 1. Circular convolution; 2. Circulant diagonalisation; 3.
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Conditions for the Existence of Fast Number Theoretic Transforms

IEEE Transactions on Computers, 1981
A new theorem that gives necessary and sufficient conditions for the existence of computationally fast number theoretic transforms is presented. The theorem combines the general conditions for the existence of number theoretic transforms in the rings of integers modulo m with two conditions for high computational efficiency.
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The eigenstructure of the number theoretic transforms

Signal Processing, 1982
Abstract Fast digital transforms are linear matrix operations and their eigenstructure is of fundamental interest. The eigensystem for the Fast Fourier transform, FFT, known for several years, can be used to design FFT algorithms. The Number Theoretic Transforms have a similar eigen problem, defined over ofZ /p which is solved in this paper. We find
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Number Theoretic Transformation Techniques

1989
Processing signals with a digital computer or with dedicated digital hardware involves the implementation of computational schemes on sequences of numbers. Practically, it is not possible to process an infinitely long sequence, although it is common practice to analyze many processing systems as though this were the case.
Robert King, Majid Ahmadi, Raouf Gorgui-Naguib, Alan Kwabwe, Mahmood Azimi-Sadjadi   +4 more
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Isomorphic number theoretic transforms

Proceedings. Electrotechnical Conference Integrating Research, Industry and Education in Energy and Communication Engineering', 2003
It is noted that the computational cost of circular convolutions can be reduced to a large extent by using number-theoretic transforms (NTTs). The author proposes a novel algorithm for removing the necessity for the transforming element of the NTT to be coincident with a power of 2.
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Microprocessor implementation of number theoretic transforms

IEE Journal on Electronic Circuits and Systems, 1979
Consideration is given to the suitability of microprocessor systems for the fast implementation of number theoretic transforms (n.t.t.s). Fast-multiply instructions available on some microprocessors, or the use of external multipliers, relax the basic constraints on the choice of a particular n.t.t.
S.C.P. Martin, B.J. Stanier
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Arithmetic for ternary number-theoretic transforms

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1993
Summary: A simplified arithmetic for the computation of ternary number-theoretic transforms is presented. The proposed arithmetic is based on the application of a code translation technique that was used by \textit{L. M. Leibowitz} [A simplified binary arithmetic for the Fermat number transform, IEEE Trans.
Sunder, S., Antoniou, A.
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Number theoretic transforms (NTTs)

2010
We introduce the number theoretic transforms (NTTs). The routines for the fast NTTs are rather straightforward translations of the FFT algorithms. Radix-2 and radix-4 routines are given, there should be no difficulty to translate any given complex FFT into the equivalent NTT.
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Number theoretic transforms for the calculation of convolutions

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
We present new algorithms for the calculation of convolutions by means of number theoretic transforms over modulo rings. Not only are these algorithms more efficient than currently used methods, but they are also very flexible. Indeed, using special algorithms for short convolutions allows trading computational efficiency for structural simplicity.
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