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Journal articles on the topic 'Circular Convolution'

Author: Grafiati

Published: 3 June 2025

Last updated: 13 July 2025

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1

Cariow, Aleksandr, and Janusz P. Paplinski. "Algorithmic Structures for Realizing Short-Length Circular Convolutions with Reduced Complexity." Electronics 10, no. 22 (2021): 2800. http://dx.doi.org/10.3390/electronics10222800.

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A set of efficient algorithmic solutions suitable to the fully parallel hardware implementation of the short-length circular convolution cores is proposed. The advantage of the presented algorithms is that they require significantly fewer multiplications as compared to the naive method of implementing this operation. During the synthesis of the presented algorithms, the matrix notation of the cyclic convolution operation was used, which made it possible to represent this operation using the matrix–vector product. The fact that the matrix multiplicand is a circulant matrix allows its successful factorization, which leads to a decrease in the number of multiplications when calculating such a product. The proposed algorithms are oriented towards a completely parallel hardware implementation, but in comparison with a naive approach to a completely parallel hardware implementation, they require a significantly smaller number of hardwired multipliers. Since the wired multiplier occupies a much larger area on the VLSI and consumes more power than the wired adder, the proposed solutions are resource efficient and energy efficient in terms of their hardware implementation. We considered circular convolutions for sequences of lengths N= 2, 3, 4, 5, 6, 7, 8, and 9.

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2

Schluttenhofer, Sandra, and Jan Johannes. "Adaptive Minimax Testing for Circular Convolution." Mathematical Methods of Statistics 29, no. 2 (2020): 106–33. http://dx.doi.org/10.3103/s1066530720020039.

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3

MILENKOVIC, VICTOR, and ELISHA SACKS. "A MONOTONIC CONVOLUTION FOR MINKOWSKI SUMS." International Journal of Computational Geometry & Applications 17, no. 04 (2007): 383–96. http://dx.doi.org/10.1142/s0218195907002392.

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We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution. The monotonic crossing number is bounded by the kinetic crossing number, and also by the maximum number of intersecting pairs of monotone boundary chains, which is typically much smaller. We give a Minkowski sum algorithm based on the monotonic convolution. The running time is O (s + nα(n) log (n) + m2), versus O (s + n2) for the kinetic algorithm, with s the input size and with n and m the number of segments in the kinetic and monotonic convolutions. For inputs with a bounded number of turning points and inflection points, the running time is O (sα(s) log s), versus Ω(s2) for the kinetic algorithm. The monotonic convolution is 37% smaller than the kinetic convolution and its arrangement is 62% smaller based on 21 test pairs.

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4

Haneda, Yoichi, Ken'ichi Furuya, Shoichi Koyama, Kenta Niwa, and Kazunori Kobayashi. "Sound field simulation for circular array based on spatial circular convolution." Acoustical Science and Technology 35, no. 2 (2014): 99–107. http://dx.doi.org/10.1250/ast.35.99.

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5

Zheng, Rong. "Design of large point circular convolution algorithm." Computer Standards & Interfaces 20, no. 6-7 (1999): 459. http://dx.doi.org/10.1016/s0920-5489(99)90986-8.

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6

Lin, Cong, Zhoujian Chen, Yiquan Huang, Haoyu Jiang, Wencai Du, and Qiong Chen. "A Deep Neural Network Based on Circular Representation for Target Detection." Journal of Sensors 2022 (April 25, 2022): 1–10. http://dx.doi.org/10.1155/2022/4437446.

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Convolutional neural network (CNN) model based on deep learning has excellent performance for target detection. However, the detection effect is poor when the object is circular or tubular because most of the existing object detection methods are based on the traditional rectangular box to detect and recognize objects. To solve the problem, we propose the circular representation structure and RepVGG module on the basis of CenterNet and expand the network prediction structure, thus proposing a high-precision and high-efficiency lightweight circular object detection method RebarDet. Specifically, circular tubular type objects will be optimized by replacing the traditional rectangular box with a circular box. Second, we improve the resolution of the network feature map and the upper limit of the number of objects detected in a single detect to achieve the expansion of the network prediction structure, optimized for the dense phenomenon that often occurs in circular tubular objects. Finally, the multibranch topology of RepVGG is introduced to sum the feature information extracted by different convolution modules, which improves the ability of the convolution module to extract information. We conducted extensive experiments on rebar datasets and used AB-Score as a new evaluation method to evaluate RebarDet. The experimental results show that RebarDet can achieve a detection accuracy of up to 0.8114 and a model inference speed of 6.9 fps while maintaining a moderate amount of parameters, which is superior to other mainstream object detection models and verifies the effectiveness of our proposed method. At the same time, RebarDet’s high precision detection of round tubular objects facilitates enterprise intelligent manufacturing processes.

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7

Lin, Cong, Zhoujian Chen, Yiquan Huang, Haoyu Jiang, Wencai Du, and Qiong Chen. "A Deep Neural Network Based on Circular Representation for Target Detection." Journal of Sensors 2022 (April 25, 2022): 1–10. http://dx.doi.org/10.1155/2022/4437446.

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Convolutional neural network (CNN) model based on deep learning has excellent performance for target detection. However, the detection effect is poor when the object is circular or tubular because most of the existing object detection methods are based on the traditional rectangular box to detect and recognize objects. To solve the problem, we propose the circular representation structure and RepVGG module on the basis of CenterNet and expand the network prediction structure, thus proposing a high-precision and high-efficiency lightweight circular object detection method RebarDet. Specifically, circular tubular type objects will be optimized by replacing the traditional rectangular box with a circular box. Second, we improve the resolution of the network feature map and the upper limit of the number of objects detected in a single detect to achieve the expansion of the network prediction structure, optimized for the dense phenomenon that often occurs in circular tubular objects. Finally, the multibranch topology of RepVGG is introduced to sum the feature information extracted by different convolution modules, which improves the ability of the convolution module to extract information. We conducted extensive experiments on rebar datasets and used AB-Score as a new evaluation method to evaluate RebarDet. The experimental results show that RebarDet can achieve a detection accuracy of up to 0.8114 and a model inference speed of 6.9 fps while maintaining a moderate amount of parameters, which is superior to other mainstream object detection models and verifies the effectiveness of our proposed method. At the same time, RebarDet’s high precision detection of round tubular objects facilitates enterprise intelligent manufacturing processes.

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8

Loulou, AlaaEddin, Juha Yli-Kaakinen, and Markku Renfors. "Advanced Low-Complexity Multicarrier Schemes Using Fast-Convolution Processing and Circular Convolution Decomposition." IEEE Transactions on Signal Processing 67, no. 9 (2019): 2304–19. http://dx.doi.org/10.1109/tsp.2019.2904015.

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9

Garg, H. K. "Skew circular convolution algorithms over finite integer rings." Electronics Letters 32, no. 24 (1996): 2213. http://dx.doi.org/10.1049/el:19961503.

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10

Lohar, G., D. P. Mukherjee, and D. Dutta Majumder. "On a decomposition of 2-D circular convolution." Pattern Recognition Letters 13, no. 10 (1992): 701–6. http://dx.doi.org/10.1016/0167-8655(92)90099-l.

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11

Recchia, Gabriel, Magnus Sahlgren, Pentti Kanerva, and Michael N. Jones. "Encoding Sequential Information in Semantic Space Models: Comparing Holographic Reduced Representation and Random Permutation." Computational Intelligence and Neuroscience 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/986574.

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Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, “noisy” permutations in which units are mapped to other units arbitrarily (no one-to-one mapping) perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.

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12

Soudris, D. J., V. Paliouras, T. Stouraitis, and A. Thanailakis. "Design methodology for the implementation of multidimensional circular convolution." IEE Proceedings - Circuits, Devices and Systems 144, no. 6 (1997): 323. http://dx.doi.org/10.1049/ip-cds:19971548.

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13

Panda, G., A. Alvarez, P. Grant, and C. Cowan. "A transform domain circular convolution algorithm for adaptive filtering." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 8 (1987): 1217–20. http://dx.doi.org/10.1109/tassp.1987.1165264.

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14

Biane, Philippe. "On the free convolution with a semi-circular distribution." Indiana University Mathematics Journal 46, no. 3 (1997): 0. http://dx.doi.org/10.1512/iumj.1997.46.1467.

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15

Chiper, Doru Florin, and Arcadie Cracan. "New Systolic Array Algorithms and VLSI Architectures for 1-D MDST." Sensors 23, no. 13 (2023): 6220. http://dx.doi.org/10.3390/s23136220.

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In this paper, we present two systolic array algorithms for efficient Very-Large-Scale Integration (VLSI) implementations of the 1-D Modified Discrete Sine Transform (MDST) using the systolic array architectural paradigm. The new algorithms decompose the computation of the MDST into modular and regular computational structures called pseudo-circular correlation and pseudo-cycle convolution. The two computational structures for pseudo-circular correlation and pseudo-cycle convolution both have the same form. This feature can be exploited to significantly reduce the hardware complexity since the two computational structures can be computed on the same linear systolic array. Moreover, the second algorithm can be used to further reduce the hardware complexity by replacing the general multipliers from the first one with multipliers with a constant that have a significantly reduced complexity. The resulting VLSI architectures have all the advantages of a cycle convolution and circular correlation based systolic implementations, such as high-speed using concurrency, an efficient use of the VLSI technology due to its local and regular interconnection topology, and low I/O cost. Moreover, in both architectures, a cost-effective application of an obfuscation technique can be achieved with low overheads.

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16

Okoloko, Innocent E. "Discrete Time Convolution is Multiplication without Carry." European Journal of Electrical Engineering and Computer Science 5, no. 5 (2021): 64–68. http://dx.doi.org/10.24018/ejece.2021.5.5.358.

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In this paper an analysis of discrete-time convolution is performed to prove that the convolution sum is polynomial multiplication without carry, whether the sequences are finite or not, by using several examples to compare the results computed using the existing approaches to the polynomial multiplication approach presented here. In the design and analysis of signals and systems the concept of convolution is very important. While software tools are available for calculating convolution, for proper understanding it is important to learn now to calculate it by hand. To this end, several popular methods are available. The idea that the convolution sum is indeed polynomial multiplication without carry is demonstrated in this paper. The concept is further extended to deconvolution, N-point circular convolution and the Z-transform approach.

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17

Gosmann, Jan, and Chris Eliasmith. "Vector-Derived Transformation Binding: An Improved Binding Operation for Deep Symbol-Like Processing in Neural Networks." Neural Computation 31, no. 5 (2019): 849–69. http://dx.doi.org/10.1162/neco_a_01179.

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We present a new binding operation, vector-derived transformation binding (VTB), for use in vector symbolic architectures (VSA). The performance of VTB is compared to circular convolution, used in holographic reduced representations (HRRs), in terms of list and stack encoding capacity. A special focus is given to the possibility of a neural implementation by the means of the Neural Engineering Framework (NEF). While the scaling of required neural resources is slightly worse for VTB, it is found to be on par with circular convolution for list encoding and better for encoding of stacks. Furthermore, VTB influences the vector length less, which also benefits a neural implementation. Consequently, we argue that VTB is an improvement over HRRs for neurally implemented VSAs.

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18

Minho Cheong and Yong-Hwan Lee. "Fast initialization of nyquist echo cancelers using circular convolution technique." IEEE Transactions on Communications 50, no. 12 (2002): 1865–70. http://dx.doi.org/10.1109/tcomm.2002.806542.

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19

Xiao, Xiangli, Junjian Huang, Yushu Zhang, and Xing He. "Efficient and Secure Outsourcing of DFT, IDFT, and Circular Convolution." IEEE Access 7 (2019): 60126–33. http://dx.doi.org/10.1109/access.2019.2915196.

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20

Yin, Xianzhe, Changli Yao, Yuanman Zheng, Wenqiang Xu, Guangxi Chen, and Xiaoyu Yuan. "A fast 3D gravity forward algorithm based on circular convolution." Computers & Geosciences 172 (March 2023): 105309. http://dx.doi.org/10.1016/j.cageo.2023.105309.

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21

Okoloko, Innocent E. "Unified Vector Multiplication Approach for Calculating Convolution and Correlation." European Journal of Engineering and Technology Research 6, no. 4 (2021): 129–34. http://dx.doi.org/10.24018/ejers.2021.6.4.2488.

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This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.

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22

Okoloko, Innocent E. "Unified Vector Multiplication Approach for Calculating Convolution and Correlation." European Journal of Engineering and Technology Research 6, no. 4 (2021): 129–34. http://dx.doi.org/10.24018/ejeng.2021.6.4.2488.

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This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.

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23

Touati, Redha, Max Mignotte, and Mohamed Dahmane. "A Circular Invariant Convolution Model-Based Mapping for Multimodal Change Detection." Advances in Science, Technology and Engineering Systems Journal 5, no. 5 (2020): 1288–98. http://dx.doi.org/10.25046/aj0505155.

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24

Taheri, Sohail, Mir Ghoraishi, Pei Xiao, and Lei Zhang. "Efficient Implementation of Filter Bank Multicarrier Systems Using Circular Fast Convolution." IEEE Access 5 (2017): 2855–69. http://dx.doi.org/10.1109/access.2017.2670922.

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25

Thomas, Lewis J. "Wall filter using circular convolution for a color flow imaging system." Journal of the Acoustical Society of America 97, no. 2 (1995): 1369. http://dx.doi.org/10.1121/1.412117.

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26

Wang, Song, and Jiankun Hu. "Design of alignment-free cancelable fingerprint templates via curtailed circular convolution." Pattern Recognition 47, no. 3 (2014): 1321–29. http://dx.doi.org/10.1016/j.patcog.2013.10.003.

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27

Yao, Qingkai, Linfang Xie, Xing Guo, Fapeng Yu, and Xian Zhao. "PVDF Membrane-Based Dual-Channel Acoustic Sensor Integrating the Fabry–Pérot and Piezoelectric Effects." Sensors 23, no. 7 (2023): 3444. http://dx.doi.org/10.3390/s23073444.

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A resonant acoustic wave detector combined with Fabry–Pérot interference (FPI) and piezoelectric (PE) effects based on a polyvinylidene fluoride (PVDF) piezoelectric film was proposed to enhance the ability of the sensor to detect acoustic signals in a specific frequency band. The deformation of circular thin films was indicated by the interference and piezoelectric effects simultaneously, and the noise level was decreased by the real-time convolution of the two-way parallel signal. This study reveals that, at the film’s resonance frequency, the minimum detection limits for the FPI and piezoelectric impacts on acoustic waves are 3.39 μPa/Hz1/2 and 20.8 μPa/Hz1/2, respectively. The convolution result shows that the background noise was reduced by 98.81% concerning the piezoelectric signal, and by 85.21% concerning the FPI signal. The convolution’s signal-to-noise ratio (SNR) was several times greater than the other two signals at 10 mPa. Therefore, this resonance sensor, which the FPI and the piezoelectric effect synergistically enhance, can be applied to scenarios of acoustic wave detection in a specific frequency band and with ultrahigh sensitivity requirements.

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28

Matthé, Maximilian, Luciano Mendes, Ivan Gaspar, Nicola Michailow, Dan Zhang, and Gerhard Fettweis. "Precoded GFDM transceiver with low complexity time domain processing." EURASIP Journal on Wireless Communications and Networking 2016, no. 1 (2016): 138. https://doi.org/10.1186/s13638-016-0633-1.

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Future wireless communication systems are demanding a more flexible physical layer. GFDM is a block filtered multicarrier modulation scheme proposed to add multiple degrees of freedom and to cover other waveforms in a single framework. In this paper, GFDM modulation and demodulation is presented as a frequency-domain circular convolution, allowing for a reduction of the implementation complexity when MF, ZF and MMSE filters are employed as linear demodulators. The frequency-domain circular convolution shows that the DFT used in the GFDM signal generation can be seen as a precoding operation. This new point-of-view opens the possibility to use other unitary transforms, further increasing the GFDM flexibility and covering a wider set of applications. The following three precoding transforms are considered in this paper to illustrate the benefits of precoded GFDM: (i) Walsh Hadamard Transform; (ii) CAZAC transform and; (iii) Discrete Hartley Transform. The PAPR and symbol error rate of these three unitary transform combined with GFDM are analyzed as well.

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29

Khan, Muhammad Ghaffar, Bakhtiar Ahmad, Basem Aref Frasin, and Thabet Abdeljawad. "On Janowski Analytic p,q-Starlike Functions in Symmetric Circular Domain." Journal of Function Spaces 2020 (October 10, 2020): 1–6. http://dx.doi.org/10.1155/2020/4257907.

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The main object of the present paper is to apply the concepts of p,q-derivative by establishing a new subclass of analytic functions connected with symmetric circular domain. Further, we investigate necessary and sufficient conditions for functions belonging to this class. Convex combination, weighted mean, arithmetic mean, growth theorem, and convolution property are also determined.

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30

Tajanpure, Rupali, and Akkalakshmi Muddana. "Circular convolution-based feature extraction algorithm for classification of high-dimensional datasets." Journal of Intelligent Systems 30, no. 1 (2021): 1026–39. http://dx.doi.org/10.1515/jisys-2020-0064.

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Abstract High-dimensional data analysis has become the most challenging task nowadays. Dimensionality reduction plays an important role here. It focuses on data features, which have proved their impact on accuracy, execution time, and space requirement. In this study, a dimensionality reduction method is proposed based on the convolution of input features. The experiments are carried out on minimal preprocessed nine benchmark datasets. Results show that the proposed method gives an average 38% feature reduction in the original dimensions. The algorithm accuracy is tested using the decision tree (DT), support vector machine (SVM), and K-nearest neighbor (KNN) classifiers and evaluated with the existing principal component analysis algorithm. The average increase in accuracy (Δ) is 8.06 for DT, 5.80 for SVM, and 18.80 for the KNN algorithm. The most significant characteristic feature of the proposed model is that it reduces attributes, leading to less computation time without loss in classifier accuracy.

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31

Song, Depeng, Binbing Li, Yi Qu, and Yijun Chen. "A circular convolution based on compressed sensing imaging algorithm for FMCW CSAR." Journal of Intelligent & Fuzzy Systems 38, no. 1 (2020): 187–96. http://dx.doi.org/10.3233/jifs-179393.

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32

Wang, L., and I. Hartimo. "Systolic realisation for 1-D circular convolution using the Chinese remainder theorem." Electronics Letters 29, no. 2 (1993): 165. http://dx.doi.org/10.1049/el:19930111.

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33

Duh, W. J., and J. L. Wu. "Two-stage circular-convolution-like algorithm/architecture for the discrete cosine transform." IEE Proceedings F Radar and Signal Processing 137, no. 6 (1990): 465. http://dx.doi.org/10.1049/ip-f-2.1990.0067.

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34

Emad Hmood Salman. "Fast Convolution and Correlation Algorithm for Multidimensional Signals." Diyala Journal of Engineering Sciences 6, no. 1 (2013): 75–89. http://dx.doi.org/10.24237/djes.2013.06107.

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The technical world is changing very rapidly. In recent three decades, the power of personal computers has increased by a factor of nearly one-thousand. By all accounts, it will increase by another factor of one-thousand in the next decade. This tremendous power has changed the way science and engineering is done, and there is no better example of this than digital signal processing (DSP). This proposal is a fast algorithm to compute some important mathematical operations in the DSP, which are the convolution and the correlation (both linear and circular). These operations are entered in most application daily computers, cellular phones, aerospace, medical devices, mechanical statuses, images processing, TV conferences, and other. Therefore, that to get at time realization system (i.e. to reduce the delay of time in any system).

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35

Vashishth, Shikhar, Soumya Sanyal, Vikram Nitin, Nilesh Agrawal, and Partha Talukdar. "InteractE: Improving Convolution-Based Knowledge Graph Embeddings by Increasing Feature Interactions." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (2020): 3009–16. http://dx.doi.org/10.1609/aaai.v34i03.5694.

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Most existing knowledge graphs suffer from incompleteness, which can be alleviated by inferring missing links based on known facts. One popular way to accomplish this is to generate low-dimensional embeddings of entities and relations, and use these to make inferences. ConvE, a recently proposed approach, applies convolutional filters on 2D reshapings of entity and relation embeddings in order to capture rich interactions between their components. However, the number of interactions that ConvE can capture is limited. In this paper, we analyze how increasing the number of these interactions affects link prediction performance, and utilize our observations to propose InteractE. InteractE is based on three key ideas – feature permutation, a novel feature reshaping, and circular convolution. Through extensive experiments, we find that InteractE outperforms state-of-the-art convolutional link prediction baselines on FB15k-237. Further, InteractE achieves an MRR score that is 9%, 7.5%, and 23% better than ConvE on the FB15k-237, WN18RR and YAGO3-10 datasets respectively. The results validate our central hypothesis – that increasing feature interaction is beneficial to link prediction performance. We make the source code of InteractE available to encourage reproducible research.

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36

Jollands, Michael C. "Assessing analytical convolution effects in diffusion studies: Applications to experimental and natural diffusion profiles." PLOS ONE 15, no. 11 (2020): e0241788. http://dx.doi.org/10.1371/journal.pone.0241788.

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Given that all in-situ analytical techniques have a non-zero beam size, all measured profiles, resulting from diffusion or otherwise, will be artefactually elongated to some degree. Profiles where the total length over which the concentration changes approaches the resolution of the analytical technique likely suffer from serious convolution; the measured profiles may be considerably elongated relative to the true profile. Resolving this effect is non-trivial, except for some specific combinations of profile type and beam geometry. In this study, a versatile method for numerically deconvoluting diffusion profiles acquired using techniques with Gaussian, Lorentzian, (pseudo-)Voigt, circular/elliptical or square/rectangular interaction volumes, is presented. A MATLAB code, including a user-friendly interface (PACE-the Program for Assessing Convolution Effects in diffusion studies), is also provided, and applied to several experimental and natural profiles interpreted as resulting from diffusion, showing various degrees of convolution.

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37

Peng, Hongli, Long Cheng, and Jianyan Tian. "Detection of Surface Defects of Barrel Media Based on PaE-VGG Model." Mathematics 13, no. 7 (2025): 1104. https://doi.org/10.3390/math13071104.

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To address the issues of insufficient defect samples and low detection accuracy of barrel media, we propose a detection of the surface defects of barrel media based on a PaE-VGG model. The proposed PaE-VGG model is based on a modification of a state-of-the-art VGG convolutional neural network, incorporating position-aware circular convolution for facilitating location-sensitive global feature extraction. For each feature extraction channel, the Efficient Channel Attention mechanism is calculated, which adaptively weights the feature vector. The experimental findings demonstrate that our proposed PaE-VGG model achieves an accuracy rate of 94.37%, showcasing a significant improvement of 4.76% compared to the previous version. Furthermore, when compared to highly successful convolutional neural networks for defect detection, such as AlexNet, Googlenet, and ResNet18, our optimization model outperforms them by 4.20%, 1.51%, and 0.72%, respectively. Therefore, the proposed PaE-VGG has achieved good precision and performance in the detection of barrel media defects after improvement.

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38

Shih-Chung B Lo, Huai Li, Yue Wang, L. Kinnard, and M. T. Freedman. "A multiple circular path convolution neural network system for detection of mammographic masses." IEEE Transactions on Medical Imaging 21, no. 2 (2002): 150–58. http://dx.doi.org/10.1109/42.993133.

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39

Zuo, Hai, Xia Lei, Rongzhen Le, and Maozhu Jin. "Signal detection through circular convolution reconstruction for OFDM system in fast varying channel." Journal of Modern Transportation 20, no. 4 (2012): 234–42. http://dx.doi.org/10.1007/bf03325804.

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40

Civalek, Ömer, and Hakan Ersoy. "Free vibration and bending analysis of circular Mindlin plates using singular convolution method." Communications in Numerical Methods in Engineering 25, no. 8 (2009): 907–22. http://dx.doi.org/10.1002/cnm.1138.

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41

Grigoryan, Artyom M., and Sos S. Agaian. "3-Qubit Circular Quantum Convolution Computation Using the Fourier Transform with Illustrative Examples." Journal of Quantum Computing 6, no. 1 (2024): 1–14. http://dx.doi.org/10.32604/jqc.2023.026981.

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42

Lu, Richard S. "Finite‐impulse‐response reduction‐to‐the‐pole filter." GEOPHYSICS 63, no. 6 (1998): 1958–64. http://dx.doi.org/10.1190/1.1444489.

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Convolving a finite‐impulse‐response (FIR) filter with a magnetic anomaly map produces a reduction‐to‐the‐pole (RTP) that is superior to that of the conventional Fourier‐transform approach. The conventional approach, in which the map’s Fourier transform is multiplied by the frequency response of the RTP filter, is flawed by not accounting properly for the dimensions of the respective Fourier transforms. The resultant wraparound effect of circular convolution degrades the RTP map. The FIR filter, combined with linear convolution and appropriate choices for dimensions of data and filter, eliminates the wraparound effect, minimizes contamination of the result by noise, and improves stability. These properties are illustrated by a synthetic example and by application to an actual data set.

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Li, Xiuyan, Yangtao Fan, Qingqing Gao, Hu Chen, and Yanhui Liu. "Identification of effects of YOYO-1 intercalation on the topological states of circular DNA." Modern Physics Letters B 32, no. 20 (2018): 1850231. http://dx.doi.org/10.1142/s0217984918502317.

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YOYO-1 intercalation leads to the reduction of twist rigidity, unwinding of DNA, elongation of DNA contour length and YOYO-1 concentration-dependent persistence length, until now few works identified their roles in determining the topological states of circular DNA. Based on the convolution of the writhe distribution of circular DNA obtained by using Monte Carlo simulation and the twist distribution, effects of YOYO-1 intercalation on the linking number distribution of circular DNA are predicted and identified. YOYO-1 intercalation leads to larger fluctuation, but not to the obvious enlargement of the writhe distribution, so that the variance of the linking number distribution mainly depends on the variance of the twist distribution. The unwinding angle contributes to the drifting of the linking number distribution away from the original equilibrium value of zero and has no effects on the variance of the linking number distribution, converse to the roles of the reduced twist rigidity in the linking number distribution. Furthermore, the method used in the work can be generalized to detect the effects of other intercalators on the topological states of circular DNA.

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Shi, Lei, Qaiser Khan, Gautam Srivastava, Jin-Lin Liu, and Muhammad Arif. "A Study of Multivalent q-starlike Functions Connected with Circular Domain." Mathematics 7, no. 8 (2019): 670. http://dx.doi.org/10.3390/math7080670.

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Starlike functions have gained popularity both in literature and in usage over the past decade. In this paper, our aim is to examine some useful problems dealing with q-starlike functions. These include the convolution problem, sufficiency criteria, coefficient estimates, and Fekete–Szegö type inequalities for a new subfamily of analytic and multivalent functions associated with circular domain. In addition, we also define and study a Bernardi integral operator in its q-extension for multivalent functions. Furthermore, we will show that the class defined in this paper, along with the obtained results, generalizes many known works available in the literature.

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Khalili, Seyyed Mohammad Reza, K. Malekzadeh, and A. Davar. "Dynamic Response of Functionally Graded Circular Cylindrical Shells." Advanced Materials Research 47-50 (June 2008): 608–11. http://dx.doi.org/10.4028/www.scientific.net/amr.47-50.608.

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In this paper the response of circular cylindrical shell made of Functionally Graded Material (FGM) subjected to lateral impulse load was investigated. The effective material properties are assumed to vary continuously along the thickness direction according to a volume fraction power law distribution. First order shear deformation theory (FSDT) and Love's first approximation theory were utilized in the equilibrium equations. The boundary condition was considered to be simply supported. Displacement components are product of functions of position and time. Equilibrium equations for free and forced vibrations were solved using the Galerkin method. The impulse load in the form of time varying uniform pressure was applied onto a small rectangular area of the shell surface. The function of time for displacement components is obtained using the results of free vibration and convolution integral. Finally time response of displacement components is derived using mode superposition method. The influence of material composition (power law exponent), geometrical parameters (length to radius and radius to thickness ratios) and load parameters (position and size of the area of the applied load and peak pressure value for different pulse type) on the dynamic response was investigated.

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Starha, Pavel, Jana Prochazkova, and Dalibor Martisek. "The Reconstruction of the Object Surface using Confocal Microscope with Hyperchromatic Lens." MENDEL 24, no. 1 (2018): 129–34. http://dx.doi.org/10.13164/mendel.2018.1.129.

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The usage of a tandem-scanning reflected-light microscope is not common but this technology offers the wide possibilities in the area of the surface reconstruction. This article presents a method that can reconstruct the 3D relief from a single image with a known calibrated set of images. The method uses the property that the points in the same height are visualized in the same color and we propose the nonlinear optimization to find this dependence. Subsequently, the low brightness parts are added by circular partial convolution.

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Li, Guoqiang, Bin Chen, Xiaobin Qi, and Lu Zhang. "Circular convolution parallel extreme learning machine for modeling boiler efficiency for a 300 MW CFBB." Soft Computing 23, no. 15 (2018): 6567–77. http://dx.doi.org/10.1007/s00500-018-3305-8.

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Yuan, Z., and X. Wang. "Non-linear buckling analysis of inclined circular cylinder-in-cylinder by the discrete singular convolution." International Journal of Non-Linear Mechanics 47, no. 6 (2012): 699–711. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.11.008.

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Civalek, Omer. "Discrete singular convolution method and applications to free vibration analysis of circular and annular plates." Structural Engineering and Mechanics 29, no. 2 (2008): 237–40. http://dx.doi.org/10.12989/sem.2008.29.2.237.

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Zhang, Wenqiong, Yiwei Huang, Jianfei Tong, Ming Bao, and Xiaodong Li. "Off-Grid DOA Estimation Based on Circularly Fully Convolutional Networks (CFCN) Using Space-Frequency Pseudo-Spectrum." Sensors 21, no. 8 (2021): 2767. http://dx.doi.org/10.3390/s21082767.

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Low-frequency multi-source direction-of-arrival (DOA) estimation has been challenging for micro-aperture arrays. Deep learning (DL)-based models have been introduced to this problem. Generally, existing DL-based methods formulate DOA estimation as a multi-label multi-classification problem. However, the accuracy of these methods is limited by the number of grids, and the performance is overly dependent on the training data set. In this paper, we propose an off-grid DL-based DOA estimation. The backbone is based on circularly fully convolutional networks (CFCN), trained by the data set labeled by space-frequency pseudo-spectra, and provides on-grid DOA proposals. Then, the regressor is developed to estimate the precise DOAs according to corresponding proposals and features. In this framework, spatial phase features are extracted by the circular convolution calculation. The improvement in spatial resolution is converted to increasing the dimensionality of features by rotating convolutional networks. This model ensures that the DOA estimations at different sub-bands have the same interpretation ability and effectively reduce network model parameters. The simulation and semi-anechoic chamber experiment results show that CFCN-based DOA is superior to existing methods in terms of generalization ability, resolution, and accuracy.

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