A new tensor product formulation for Toom's convolution algorithm

Elnaggar, A.; Alouweiri, H.M.; Ito, M.R.

doi:10.1109/78.752626

Cited by 8 publications

(9 citation statements)

References 6 publications

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“…Therefore, the total number of multiplications required is equal to the number of multiplications in the single-core stage and is equal to [1]. Tables I and II show the computational advantage of the proposed improved algorithm when compared to previous algorithms, such as the original matrix-vector multiplication and the fast Fourier transform (FFT) algorithms.…”

Section: Multiplexed Architecture Of the 1-d Convolutionmentioning

confidence: 94%

“…The proposed work is based on a nontrivial modification of the one-dimensional (1-D) convolution algorithm presented in [1] and shown in Fig. 1.…”

mentioning

confidence: 99%

“…The linear convolution in matrix form is given by , where is the convolution matrix defined by [1] ( …”

mentioning

confidence: 99%

“…Many approaches have been suggested to achieve high-speed processing for linear convolution and to design efficient convolution architectures [1]- [5].…”

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confidence: 99%

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An improved Toom's algorithm for linear convolution

Elnaggar

Aboelaze

2002

IEEE Signal Process. Lett.

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Abstract-This letter presents an improved Toom's algorithm that allows hardware savings without slowing down the processing speed. We derive formulae for the number of multiplications and additions required to compute the linear convolution of size = 2 . We demonstrate the computational advantage of the proposed improved algorithm when compared to previous algorithms, such as the original matrix-vector multiplication and the FFT algorithms.

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Section: Multiplexed Architecture Of the 1-d Convolutionmentioning

confidence: 94%

“…The proposed work is based on a nontrivial modification of the one-dimensional (1-D) convolution algorithm presented in [1] and shown in Fig. 1.…”

mentioning

confidence: 99%

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An improved Toom's algorithm for linear convolution

Elnaggar

Aboelaze

2002

IEEE Signal Process. Lett.

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“…We employ several techniques to manipulate such decompositions into suitable expressions that can be mapped efficiently onto very large scale integration (VLSI) structures. Tensor products (or Kronecker products), when coupled with permutation matrices, have proven to be useful in providing a unified decomposable matrix, formulations for multidimensional transforms, convolutions, matrix multiplication, and other fundamental computations [2], [3], [6].…”

Section: Introductionmentioning

confidence: 99%

An efficient architecture for multi-dimensional convolution

Elnaggar

Aboelaze

2000

IEEE Trans. Circuits Syst. II

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This paper presents modified parallel architectures for multidimensional (-d) convolution. We show that for two-dimensional (2-d) convolutions, with careful design, the number of lower-order 2-d convolutions can be reduced from nine to six with a computation saving of 33%. Moreover, the original speed of the computations is not affected. The proposed partitioning strategy results in a core of data-independent convolution computations, and can be generalized to the-d convolution. The resulting very large scale integration networks have very simple modular structure, highly regular topology, and use simple arithmetic devices.

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