Novel Convolutions Using First-Order Moments

Liu, Jianguo; Pan, Chao; Liu, Zhenbing

doi:10.1109/tc.2011.126

Cited by 7 publications

(6 citation statements)

References 18 publications

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“…Liu et al presented an algorithm and its systolic array for first-order moment in [25][26][27]. Their method is suitable to compute the first-order and the zero-order moment in Equation (4) rapidly.…”

Section: The Fast Algorithm and Systolic Array For First-order Momentmentioning

confidence: 99%

“…According to [25], we illustrate a simple 1-network shown in Figure 1 that represents a map of transforming the two-dimensional vector (1, x) into the vector (1, (1 + x)). This map is denoted by F that is Some characteristic equations obtained from F are…”

Section: The Fast Algorithm For First-order Momentmentioning

confidence: 99%

“…It is a breakthrough that an NCC formula expressed in terms of a first-order moment is designed according to the relationship between the inner-product and the first-order moment, so the computational complexity of NCC is transformed into that of a first-order moment. For performing an arbitrary-length digital NCC, our algorithm would first establish the NCC formula based on a first-order moment for correlation sequences, and then introduce a fast algorithm without multiplication from [25,26] to compute this first-order moment in the new NCC formula rapidly. For the hardware implementation of NCC, we develop a simple and scalable systolic array derived from the proposed algorithm, due to the fact that the fast algorithm for the first-order moment is easily performed by systolic structure [27].…”

Section: Introductionmentioning

confidence: 99%

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The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

Pan

Xia

et al. 2020

Sensors

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Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.

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Section: The Fast Algorithm and Systolic Array For First-order Momentmentioning

confidence: 99%

Section: The Fast Algorithm For First-order Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

Pan

Xia

et al. 2020

Sensors

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“…The digital convolutions using the first-order moments has been proposed [13], and the method that based on the firstorder moments can be applied in the discrete H transforms similarly. We first divide the input index set {0,1,2,…,N-1} into L parts.…”

Section: The First-order Moments Based Algorithmmentioning

confidence: 99%

A novel fast algorithm for discrete Hartley transform of type-III base on the split-radix and first-order moments

Xia

Liu

2013

SPIE Proceedings

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This paper introduces and evaluates a new algorithm for the computation of type-III discrete Hartley transforms (DHT) of length N = 2 n . The length-N type-III discrete Hartley transforms can be decomposed into several length-16 type-III discrete Hartley transforms based on the radix-2 fast algorithm, and the length-16 type-III discrete Hartley transforms can be computed by first-order moments. It can save a lot of arithmetic operations and the computational complexity of the algorithms is lower than some existing methods. Moreover, this algorithm can be easily implemented. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/24/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 8920 892007-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/24/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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“…But to achieve the highest efficiency, all the above methods require that the signal length N is highly composite, and the error of DHT is not considered. In this paper, based on our work in [4,15,16], we proposed a multiplierless algorithm for arbitrary length DHT, which transforms the multiplications of our moments-based DHT into additions by shifting digits and accumulation of integers. Based on the approach to the fast calculation of moments [4], systolic arrays to perform 1-D DHT are presented, followed by a complexity analysis.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary-length Fast Hartley Transform without Multiplications

Liu¹,

Jiang²,

Yang³

et al. 2013

JCP

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Discrete Hartley transform (DHT) is an important tool in digital signal processing. In this paper, a multilierless algorithm to compute discrete Hartley transforms is proposed, which can deal with arbitrary length input signals. The proposed algorithm can be implemented by integer additions of fixed points in binary system. Besides, an efficient and regular systolic array is designed to implement the proposed method, followed by the complexity analysis. Being different to other fast Hartley transforms, our algorithm can deal with arbitrary length signals and get high precision. The proposed method is easily implemented by hardware and very suited to a realtime processing.

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Novel Convolutions Using First-Order Moments

Cited by 7 publications

References 18 publications

The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

A novel fast algorithm for discrete Hartley transform of type-III base on the split-radix and first-order moments

Arbitrary-length Fast Hartley Transform without Multiplications

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