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Journal articles on the topic 'Linear Convolution'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Narasimha, Madihally J. "Linear Convolution Using Skew-Cyclic Convolutions." IEEE Signal Processing Letters 14, no. 3 (2007): 173–76. http://dx.doi.org/10.1109/lsp.2006.884034.

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2

Pupeikis, Rimantas. "Revised linear convolution." Lietuvos matematikos rinkinys 60 (November 12, 2019): 33–38. http://dx.doi.org/10.15388/lmr.a.2019.14959.

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It is assumed that linear time-invariant (LTI) system input signal samples are updated by a sensor in real time. It is urgent for every new input sample or for small part of new samples to update an ordinary convolution as well. The idea is that well-known convolution sum algorithm, used to calculate output signal, should not be recalculated with every new input sample. It is necessary just to modify the algorithm, when the new input sample renew the set of previous samples. Approaches in time and frequency domains are analyzed. An example of computation of the convolution in time area is pres

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3

Zhang, Xin, Yingze Song, Tingting Song, et al. "LDConv: Linear deformable convolution for improving convolutional neural networks." Image and Vision Computing 149 (September 2024): 105190. http://dx.doi.org/10.1016/j.imavis.2024.105190.

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4

Stone, H. S. "Convolution theorems for linear transforms." IEEE Transactions on Signal Processing 46, no. 10 (1998): 2819–21. http://dx.doi.org/10.1109/78.720385.

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5

Kurakin, V. L. "Convolution of linear recurrent sequences." Russian Mathematical Surveys 48, no. 4 (1993): 249–50. http://dx.doi.org/10.1070/rm1993v048n04abeh001060.

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6

Moyo, Lloyd Edgar S. "Codomains for the Cauchy-Riemann and Laplace operators inℝ2". Journal of Function Spaces and Applications 6, № 1 (2008): 71–87. http://dx.doi.org/10.1155/2008/837415.

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A codomain for a nonzero constant-coefficient linear partial differential operatorP(∂)with fundamental solutionEis a space of distributionsTfor which it is possible to define the convolutionE*Tand thus solving the equationP(∂)S=T. We identify codomains for the Cauchy-Riemann operator inℝ2and Laplace operator inℝ2. The convolution is understood in the sense of theS′-convolution.

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7

Dharani Sri, Vuyyuru. "Road Extraction from Remote Sensing Images Using a Skip-Connected Parallel CNN-Transformer Encoder-Decoder Model." INTERNATIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 09, no. 05 (2025): 1–9. https://doi.org/10.55041/ijsrem49159.

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Abstract - Extracting roads from remote sensing images holds significant practical value across fields like urban planning, traffic management, and disaster monitoring. Current Convolutional Neural Network (CNN) methods, praised for their robust local feature learning enabled by inductive biases, deliver impressive results. However, they face challenges in capturing global context and accurately extracting the linear features of roads due to their localized receptive fields. To address these shortcomings of traditional methods, this paper proposes a novel parallel encoder architecture that int

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8

Hari Kishore, K., Fazal Noorbasha, Katta Sandeep, D. N. V. Bhupesh, SK Khadar Imran, and K. Sowmya. "Linear convolution using UT Vedic multiplier." International Journal of Engineering & Technology 7, no. 2.8 (2018): 409. http://dx.doi.org/10.14419/ijet.v7i2.8.10471.

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Linear Convolution is one of the elemental operations of Signal processing systems and is used by some Multiplication Algorithms. In our project we perform Linear Convolution using ancient Multiplication Algorithm called UrdhvaTriyagbhyam (UT) which is one among the 16 sutras in Vedic mathematics. This provides best results in speed when compared to other multipliers. UrdhvaTriyagbhyam technique is used to increase the timing performance of the design. Our aim is to design 8 bit convolution using UT. The synthesis and simulation is done by using XILINX ISE Design.

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Li, Shang, Fei Yu, Shankou Zhang, Huige Yin, and Hairong Lin. "Optimization of Direct Convolution Algorithms on ARM Processors for Deep Learning Inference." Mathematics 13, no. 5 (2025): 787. https://doi.org/10.3390/math13050787.

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In deep learning, convolutional layers typically bear the majority of the computational workload and are often the primary contributors to performance bottlenecks. The widely used convolution algorithm is based on the IM2COL transform to take advantage of the highly optimized GEMM (General Matrix Multiplication) kernel acceleration, using the highly optimized BLAS (Basic Linear Algebra Subroutine) library, which tends to incur additional memory overhead. Recent studies have indicated that direct convolution approaches can outperform traditional convolution implementations without additional me

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10

Chen, Lei, Le Wu, Richang Hong, Kun Zhang, and Meng Wang. "Revisiting Graph Based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 01 (2020): 27–34. http://dx.doi.org/10.1609/aaai.v34i01.5330.

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Graph Convolutional Networks~(GCNs) are state-of-the-art graph based representation learning models by iteratively stacking multiple layers of convolution aggregation operations and non-linear activation operations. Recently, in Collaborative Filtering~(CF) based Recommender Systems~(RS), by treating the user-item interaction behavior as a bipartite graph, some researchers model higher-layer collaborative signals with GCNs. These GCN based recommender models show superior performance compared to traditional works. However, these models suffer from training difficulty with non-linear activation

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11

Fan, Yuchen, Jiahui Yu, Ding Liu, and Thomas S. Huang. "Scale-Wise Convolution for Image Restoration." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (2020): 10770–77. http://dx.doi.org/10.1609/aaai.v34i07.6706.

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While scale-invariant modeling has substantially boosted the performance of visual recognition tasks, it remains largely under-explored in deep networks based image restoration. Naively applying those scale-invariant techniques (e.g., multi-scale testing, random-scale data augmentation) to image restoration tasks usually leads to inferior performance. In this paper, we show that properly modeling scale-invariance into neural networks can bring significant benefits to image restoration performance. Inspired from spatial-wise convolution for shift-invariance, “scale-wise convolution” is proposed

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12

Margrave, Gary F. "Theory of nonstationary linear filtering in the Fourier domain with application to time‐variant filtering." GEOPHYSICS 63, no. 1 (1998): 244–59. http://dx.doi.org/10.1190/1.1444318.

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A general linear theory describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier transforms or generalized convolutional integrals. Nonstationary transforms such as the wavelet transform are not required. There are many possible applications of this theory including: the one‐way propagation of waves through complex media,

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13

Wellington, Paul, Romain Brossier, Okba Hamitou, Phuong-Thu Trinh, and Jean Virieux. "Efficient anisotropic dip filtering via inverse correlation functions." GEOPHYSICS 82, no. 4 (2017): A31—A35. http://dx.doi.org/10.1190/geo2016-0552.1.

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We have developed a computational framework that allows an efficient, spatially variant correlation filter for anisotropic dip filtering. The approach is based on the Laplace correlation function, for which there exists analytical expressions for the correlation kernel and its inverse kernel in the 1D case. An extension to higher dimensions by adding orthogonal 1D inverse functions provides a linear equation whose solution is identical to applying a Bessel filter. We have found that a good approximation of the Laplace filter function is obtained by applying a cascade of Bessel filters. We impl

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14

Ding, Chen, Xu Li, Jingyi Chen, Yaoyang Xu, Mengmeng Zheng, and Lei Zhang. "Hyperspectral Image Classification Promotion Using Dynamic Convolution Based on Structural Re-Parameterization." Remote Sensing 15, no. 23 (2023): 5561. http://dx.doi.org/10.3390/rs15235561.

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In a hyperspectral image classification (HSIC) task, manually labeling samples requires a lot of manpower and material resources. Therefore, it is of great significance to use small samples to achieve the HSIC task. Recently, convolutional neural networks (CNNs) have shown remarkable performance in HSIC, but they still have some areas for improvement. (1) Convolutional kernel weights are determined through initialization and cannot be adaptively adjusted based on the input data. Therefore, it is difficult to adaptively learn the structural features of the input data. (2) The convolutional kern

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15

Reddy, Bharathi, D. Leela Rani, and Prof S. Varadarajan. "HIGH SPEED CARRY SAVE MULTIPLIER BASED LINEAR CONVOLUTION USING VEDIC MATHAMATICS." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 4, no. 2 (2013): 284–87. http://dx.doi.org/10.24297/ijct.v4i2a2.3173.

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VLSI applications include Digital Signal Processing, Digital control systems, Telecommunications, Speech and Audio processing for audiology and speech language pathology. The latest research in VLSI is the design and implementation of DSP systems which are essential for above applications. The fundamental computation in DSP Systems is convolution. Convolution and LTI systems are the heart and soul of DSP. The behavior of LTI systems in continuous time is described by Convolution integral whereas the behavior in discrete-time is described by Linear convolution. In this paper, Linear convolution

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16

Dmitriev, M. G., and V. A. Lomazov. "Sensitivity of Linear Convolution from Expert Judgments." Procedia Computer Science 31 (2014): 802–6. http://dx.doi.org/10.1016/j.procs.2014.05.330.

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17

Mäkilä, P. M. "When is a linear convolution system stabilizable?" Systems & Control Letters 46, no. 5 (2002): 371–78. http://dx.doi.org/10.1016/s0167-6911(02)00161-5.

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18

Elnaggar, A., and M. Aboelaze. "An improved Toom's algorithm for linear convolution." IEEE Signal Processing Letters 9, no. 7 (2002): 211–14. http://dx.doi.org/10.1109/lsp.2002.801718.

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19

Chang, Mei-Chu. "Convolution of discrete measures on linear groups." Journal of Functional Analysis 247, no. 2 (2007): 417–37. http://dx.doi.org/10.1016/j.jfa.2007.03.017.

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20

Kumar, Tanuj, and Akhilesh Prasad. "Convolution with the linear canonical Hankel transformation." Boletín de la Sociedad Matemática Mexicana 25, no. 1 (2017): 195–213. http://dx.doi.org/10.1007/s40590-017-0187-1.

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21

Sandberg, Irwin W. "A representation theorem for linear discrete-space systems." Mathematical Problems in Engineering 4, no. 5 (1998): 369–75. http://dx.doi.org/10.1155/s1024123x98000878.

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The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output mapHthat can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.

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22

Prabha, Sivaraman Nair. "Convolution identities of p-numbers." Mathematica Montisnigri 61 (2024): 26–43. https://doi.org/10.20948/mathmontis-2024-61-3.

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In this paper, we derive some convolution identities for p-numbers: Fibonacci p-numbers Fp (n), Lucas p-numbers Lp (n), Jacobsthal p-numbers Jp (n), Jacobsthal-Lucas p-numbers jp (n) and Leonardo p-numbers ℒp (n), which are generalizations of the “usual” Fibonacci, Lucas, Jacobsthal, Jacobsthal-Lucas and Leonardo numbers. For p > 0, the nth Fibonacci p-number Fp (n) is defined by the linear recurrence Fp (n) = Fp (n – 1) + Fp (n – p – 1) for n > p with initial values Fp (0) = 0 and Fp (1) = Fp (2)= ⋅⋅⋅ = Fp (p) = 1, and the nth Lucas p-number Lp (n) is defined by the linear recurrence Lp

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23

Wang, Rongbo, and Qiang Feng. "Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application." Axioms 13, no. 6 (2024): 402. http://dx.doi.org/10.3390/axioms13060402.

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Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we ut

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24

Kunwar, B. "Some Direct Estimates for Linear Combination of Linear Positive Convolution Operators." Applied and Computational Mathematics 5, no. 5 (2016): 207. http://dx.doi.org/10.11648/j.acm.20160505.14.

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25

Bahri, Mawardi, and Ryuichi Ashino. "A Convolution Theorem Related to Quaternion Linear Canonical Transform." Abstract and Applied Analysis 2019 (May 28, 2019): 1–9. http://dx.doi.org/10.1155/2019/3749387.

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We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain we derive the convolution theorem associated with the QLCT and obtain a few consequences.

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26

Ricci, Paolo Emilio, and Pierpaolo Natalini. "General Linear Recurrence Sequences and Their Convolution Formulas." Axioms 8, no. 4 (2019): 132. http://dx.doi.org/10.3390/axioms8040132.

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We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.

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27

Capobianco, Giovanni, Carmine Cerrone, Andrea Di Placido, et al. "Image convolution: a linear programming approach for filters design." Soft Computing 25, no. 14 (2021): 8941–56. http://dx.doi.org/10.1007/s00500-021-05783-5.

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AbstractImage analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques. Convolution is a technique used to enhance specific characteristics of an image, while deconvolution is its inverse process. In this work, we focus on the deconvolution process, defining a new approach to retrieve filters applied in the convolution phase. Given an image I and a filtered image $$I' = f(I)$$ I ′ = f ( I ) , we propose three mathematical formulations that, starting from I and $$I'$$ I ′ , are able to identify the f

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28

Poliarus, Oleksandr, Yana Medvedovska, Yevhen Poliakov, Yevhenii Chepusenko, and Yurii Zharko. "SIMPLIFIED MODEL OF LINEAR INERTIAL MEASUREMENT SYSTEMS." Bulletin of Kharkov National Automobile and Highway University 1, no. 92 (2021): 119. http://dx.doi.org/10.30977/bul.2219-5548.2021.92.0.119.

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Problem. To increase the metrological reliability of measuring systems at technical objects, the number of sensors measuring the same process parameter is increased to several units and a model of a multi-channel measuring system is synthesized. This synthesis is usually based on the use of Markov's theory of linear filtering, but the presence of a connection between the input and output signals of the linear inertial system through the convolution integral significantly complicates the process of obtaining the optimal device. Goal. The aim of the article is to develop a method for approximati

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29

Liu, Jin-Lin, and Shigeyoshi Owa. "On a class of meromorphicp-valent starlike functions involving certain linear operators." International Journal of Mathematics and Mathematical Sciences 32, no. 5 (2002): 271–80. http://dx.doi.org/10.1155/s016117120220335x.

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Let∑pbe the class of functionsf(z)which are analytic in the punctured disk𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operatorDn+pdefined by using the convolutions, the subclass𝒯n+p(α)of∑pis considered. The object of the present paper is to prove that𝒯n+p(α)⊂𝒯n+p−1(α). Since𝒯0(α)is the class of meromorphicp-valent starlike functions of orderα, all functions in𝒯n+p−1(α)are meromorphicp-valent starlike in the open unit disk𝔼. Further properties preserving integrals and convolution conditions are also considered.

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30

Oktaviana, W., S. Musdalifah, and Resnawati. "Modifikasi Teorema Konvolusi Transformasi Kanonikal Linier Quaternion Sisi Kiri." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 16, no. 2 (2020): 116–25. http://dx.doi.org/10.22487/2540766x.2019.v16.i2.14993.

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ABSTRACTQuaternion Linear Canonical Transform (QLCT) is a generalization of the Linear Canonical Transform (LCT) onquaternion algebra which plays an important role in optics and signal processing. QLCT can be seen asgeneralization of Quaternion Fourier Transform (QFT). Based on the fact, this paper propose the formulat ofmodification convolution theorem based on left-sided QLCT by considering the fundamental relationship betweenleft-sided QLCT and QFT. The results showed the modification convolution theorem for left-sided QLCT based onrelationship between left-sided QLCT and QFT as a sum of mu

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31

Gao, Wen-Biao. "Discrete Octonion Linear Canonical Transform: Definition and Properties." Fractal and Fractional 8, no. 3 (2024): 154. http://dx.doi.org/10.3390/fractalfract8030154.

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In this paper, the discrete octonion linear canonical transform (DOCLCT) is defined. According to the definition of the DOCLCT, some properties associated with the DOCLCT are explored, such as linearity, scaling, boundedness, Plancherel theorem, inversion transform and shift transform. Then, the relationship between the DOCLCT and the three-dimensional (3-D) discrete linear canonical transform (DLCT) is obtained. Moreover, based on a new convolution operator, we derive the convolution theorem of the DOCLCT. Finally, the correlation theorem of the DOCLCT is established.

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32

Marsi, Stefano, Jhilik Bhattacharya, Romina Molina, and Giovanni Ramponi. "A Non-Linear Convolution Network for Image Processing." Electronics 10, no. 2 (2021): 201. http://dx.doi.org/10.3390/electronics10020201.

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This paper proposes a new neural network structure for image processing whose convolutional layers, instead of using kernels with fixed coefficients, use space-variant coefficients. The adoption of this strategy allows the system to adapt its behavior according to the spatial characteristics of the input data. This type of layers performs, as we demonstrate, a non-linear transfer function. The features generated by these layers, compared to the ones generated by canonical CNN layers, are more complex and more suitable to fit to the local characteristics of the images. Networks composed by thes

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33

El Jaafari, Ilyas, Ayoub Ellahyani, and Said Charfi. "Rectified non-linear unit for convolution neural network." Journal of Physics: Conference Series 1743 (January 2021): 012014. http://dx.doi.org/10.1088/1742-6596/1743/1/012014.

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34

Cariow, Aleksandr, and Janusz P. Paplinski. "Some Algorithms for Computing Short-Length Linear Convolution." Electronics 9, no. 12 (2020): 2115. http://dx.doi.org/10.3390/electronics9122115.

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In this article, we propose a set of efficient algorithmic solutions for computing short linear convolutions focused on hardware implementation in VLSI. We consider convolutions for sequences of length N= 2, 3, 4, 5, 6, 7, and 8. Hardwired units that implement these algorithms can be used as building blocks when designing VLSI -based accelerators for more complex data processing systems. The proposed algorithms are focused on fully parallel hardware implementation, but compared to the naive approach to fully parallel hardware implementation, they require from 25% to about 60% less, depending o

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35

Elnaggar, A., M. Aboelaze, and A. Al-Naamany. "A modified shuffle-free architecture for linear convolution." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 48, no. 9 (2001): 862–66. http://dx.doi.org/10.1109/82.965001.

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36

Wang Shu and Yao Tianren. "Algorithm for linear convolution using number theoretic transforms." Electronics Letters 24, no. 5 (1988): 249. http://dx.doi.org/10.1049/el:19880167.

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37

Szakács, Tamás. "Convolution of second order linear recursive sequences II." Communications in Mathematics 25, no. 2 (2017): 137–48. http://dx.doi.org/10.1515/cm-2017-0011.

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Abstract We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

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38

Vogt, L. "Approximation by linear combinations of positive convolution integrals." Journal of Approximation Theory 57, no. 2 (1989): 178–201. http://dx.doi.org/10.1016/0021-9045(89)90055-5.

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39

Wilson, D. A. "Convolution and Hankel operator norms for linear systems." IEEE Transactions on Automatic Control 34, no. 1 (1989): 94–97. http://dx.doi.org/10.1109/9.8655.

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40

Chellaboina, VijaySekhar, Wassim M. Haddad, Dennis S. Bernstein, and David A. Wilson. "Induced Convolution Operator Norms of Linear Dynamical Systems." Mathematics of Control, Signals, and Systems 13, no. 3 (2000): 216–39. http://dx.doi.org/10.1007/pl00009868.

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41

Chang, Mei-Chu. "WITHDRAWN: Convolution of discrete measures on linear groups." Journal of Functional Analysis 253, no. 1 (2007): 303–23. http://dx.doi.org/10.1016/j.jfa.2007.03.008.

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42

Székely, Vladimír, and Albin Szalai. "Transformation between linear network features in convolution approach." International Journal of Circuit Theory and Applications 43, no. 1 (2013): 94–110. http://dx.doi.org/10.1002/cta.1928.

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43

Bahri, Mawardi, and Ryuichi Ashino. "Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle." Journal of Mathematics 2019 (September 9, 2019): 1–13. http://dx.doi.org/10.1155/2019/1062979.

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A definition of the two-dimensional quaternion linear canonical transform (QLCT) is proposed. The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the definition of the classical linear canonical transform (LCT). Several useful properties of the QLCT are obtained from the properties of the QLCT kernel. Based on the convolutions and correlations of the LCT and QFT, convolution and correlation theorems associated with the QLCT are studied. An uncertainty principle for the QLCT is established. It is shown that the localiza

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44

Purwono, Purwono, Alfian Ma'arif, Wahyu Rahmaniar, Haris Imam Karim Fathurrahman, Aufaclav Zatu Kusuma Frisky, and Qazi Mazhar ul Haq. "Understanding of Convolutional Neural Network (CNN): A Review." International Journal of Robotics and Control Systems 2, no. 4 (2023): 739–48. http://dx.doi.org/10.31763/ijrcs.v2i4.888.

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The application of deep learning technology has increased rapidly in recent years. Technologies in deep learning increasingly emulate natural human abilities, such as knowledge learning, problem-solving, and decision-making. In general, deep learning can carry out self-training without repetitive programming by humans. Convolutional neural networks (CNNs) are deep learning algorithms commonly used in wide applications. CNN is often used for image classification, segmentation, object detection, video processing, natural language processing, and speech recognition. CNN has four layers: convoluti

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45

Hale, Nicholas. "An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type." IMA Journal of Numerical Analysis 39, no. 4 (2018): 1727–46. http://dx.doi.org/10.1093/imanum/dry042.

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Abstract The Legendre-based ultraspherical spectral method for ordinary differential equations (Olver, S. & Townsend, A. (2013) A fast and well-conditioned spectral method. SIAM Rev., 55, 462–489.) is combined with a formula for the convolution of two Legendre series (Hale, N. & Townsend, A. (2014a) An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 36, A1207–A1220.) to produce a new technique for solving linear Fredholm and Volterra integro-differential equations with convolution-type kernels. When the kernel and coefficient functions are sufficiently smooth, t

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46

Liu, Shao Gang, and Qiu Jin. "Tolerance Analysis Method Using Improved Convolution Method." Applied Mechanics and Materials 271-272 (December 2012): 1463–66. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.1463.

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Convolution method is studied to analyze statistical tolerance for linear dimension chain and nonlinear dimension chain. Hybrid convolution method is proposed, which is the integration of analytical convolution and numerical convolution. In order to reduce the algorithm errors, improved convolution method is proposed. Comparing with other statistical tolerance analysis methods, this method is faster and accurate. At last, an example is used to demonstrate the method proposed in this paper.

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47

Thao, Nguyen Xuan, and Hoang Tung. "The h-Fourier cosine-Laplace generalized convolution with a weight function." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 54 (2023): 321–40. https://doi.org/10.71352/ac.54.321.

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We construct h-Fourier cosine-Laplace discrete generalized convolution with a weight function on time scale {T}_h^0 and study its properties. We obtain some inequalities for this generalized convolution such as Young's type inequalities, Saitoh's type inequalities. In the application, we apply this generalized convolution to solve some linear equations of generalized convolution type.

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48

Sharma, Poonam, Ravinder Krishna Raina, and Janusz Sokół. "On a Generalized Convolution Operator." Symmetry 13, no. 11 (2021): 2141. http://dx.doi.org/10.3390/sym13112141.

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Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic fun

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Kang, Yangyuxuan, Yuyang Liu, Anbang Yao, Shandong Wang, and Enhua Wu. "3D Human Pose Lifting with Grid Convolution." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 1 (2023): 1105–13. http://dx.doi.org/10.1609/aaai.v37i1.25192.

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Existing lifting networks for regressing 3D human poses from 2D single-view poses are typically constructed with linear layers based on graph-structured representation learning. In sharp contrast to them, this paper presents Grid Convolution (GridConv), mimicking the wisdom of regular convolution operations in image space. GridConv is based on a novel Semantic Grid Transformation (SGT) which leverages a binary assignment matrix to map the irregular graph-structured human pose onto a regular weave-like grid pose representation joint by joint, enabling layer-wise feature learning with GridConv o

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Bahri, Mawardi, Samsul Ariffin Abdul Karim, Bannu Addul S., Muhammad Nur, and Nurwahidah Nurwahidah. "A New Form of Convolution Theorem for One-Dimensional Quaternion Linear Canonical Transform and Application." Symmetry 17, no. 7 (2025): 1004. https://doi.org/10.3390/sym17071004.

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In this research work, we focus on the one-dimensional quaternion linear canonical transform (1-D QLCT). Under certain conditions, we first derive the symmetry property of the 1-D QLCT for real signals. The new form of the convolution theorem related to this transformation is proposed. We develop this convolution definition to derive the correlation theorem for the 1-D QLCT. We then show that the direct connection between the quaternion convolution and quaternion correlation definitions permits us to provide a different way for proving the correlation theorem concerning the 1-D QLCT. Finally,

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