Rader–Brenner Algorithm for Computing New Mersenne Number Transform

Boussakta, S.; Hamood, M. T.

doi:10.1109/tcsii.2011.2158714

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…6,7 Specifically, the FNT length can be power of two, then the multiplication can be replaced by the shift-addition operation, resulting in faster computation than conventional FFT or Hartley transform. 12 However, our study will show that the realization complexity of NMNT can be further reduced. Moreover, there are many strict restrictions on NMT, such as length and kernel number, leading to the fact that the transform length cannot be power of two.…”

Section: Introductionmentioning

confidence: 80%

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A fast realization of new Mersenne number transformation and its applications

Hua

Liu

et al. 2019

Circuit Theory & Apps

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The new Mersenne number transform (NMNT) can be realized by the fast Fourier transform (FFT) with power-of-two length, which results in great flexibility in real-world fixed-point computations, such as the convolution-based signal processing in the embedded device. Yet the FFT realization exists the truncation errors and in order to further reduce the computations, this paper puts forward a novel realization structure for the NMNT, where the Walsh-Hadamard transform (WHT) is employed to accelerate the NMNT computation. Moreover, we also propose the refined computing structure using the matrix decomposition and multiple constant multiplication (MCM), and then all multiplications can be replaced by the shift-addition operations without precision loss. Besides, the use of lookup table (LUT) to reduce the complexity is also discussed in our study. A typical convolution application is tested by computer simulations, while the result demonstrates that the proposed scheme produces precise computing results with reduced complexity. KEYWORDS computing complexity, fast realization, Walsh-Hadamard new mersenne number transform, Walsh Hadamard transform 738

show abstract

Section: Introductionmentioning

confidence: 80%

“…The fast realization of NMNT could be found as the radix-2 NMNT, 10 radix-4 NMNT, 11 and the Rader-Brenner NMNT. 12 However, our study will show that the realization complexity of NMNT can be further reduced.…”

Section: Introductionmentioning

confidence: 80%

A fast realization of new Mersenne number transformation and its applications

Hua

Liu

et al. 2019

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…Particularly, when NTTs are employed, floating-point operations and rounding-off errors are avoided. This allows faster and cheaper hardware implementations [3,4].…”

mentioning

confidence: 99%

Fast algorithm for computing cosine number transform

Lima

2015

Electron. lett.

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A fast algorithm for the computation of a cosine-like number-theoretic transform is presented. The method, which corresponds to a finite field extension of a method originally designed for computing real-valued discrete cosine transforms, is recursive and suitable for VLSI implementation. A general flow diagram for the proposed algorithm is given and shows that, in some specific cases, it can be evaluated using additions and bit-shift operations only.

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Hardware Architectures for Computing 8-Point Cosine Number Transform

Neto

Lima

2018

2018 IEEE International Symposium on Circuits and Systems (ISCAS)

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Rader–Brenner Algorithm for Computing New Mersenne Number Transform

Cited by 3 publications

References 19 publications

A fast realization of new Mersenne number transformation and its applications

A fast realization of new Mersenne number transformation and its applications

Fast algorithm for computing cosine number transform

Hardware Architectures for Computing 8-Point Cosine Number Transform

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