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Journal articles on the topic 'Walsh matrix'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Wan, K. F., P. C. Ching, and C. K. Li. "A Set of Split-Matrix Ordered Walsh Functions." Journal of Circuits, Systems and Computers 07, no. 06 (1997): 537–42. http://dx.doi.org/10.1142/s0218126697000401.

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A new set of Walsh functions is defined in terms of the split-matrix ordering. The intrinsic properties of the functions are analyzed. The relationship and the associated conversion rules between the newly defined functions and other typical Walsh functions are discussed. It is shown that the proposed Walsh functions provide a straighforward and efficient algorithm for fast Discrete Walsh Transformation.

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Беспалов, М. С., and К. А. Фролов. "Information encoding by linear permutations of discrete Walsh transform." Proceedings in Cybernetics 23, no. 3 (2024): 90–95. https://doi.org/10.35266/1999-7604-2024-3-10.

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The paper proposes a method for using a code matrix as a private key for the Walsh-Hadamard code. The number of possible code matrices has been calculated. For example, there are almost 10 million possible keys for a Walsh matrix of the order 32, they are also level 5. The paper describes the method of decoding information and the procedure for isolating the code matrix from the encrypted Walsh matrix.

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ASAHI, Hideyasu. "A Function Generator for Walsh Order Hadamard Matrix and Fast Walsh-Hadamard Transform." Geoinformatics 11, no. 1 (2000): 3–9. http://dx.doi.org/10.6010/geoinformatics1990.11.1_3.

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4

Tsuneda, Akio. "Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions." Entropy 21, no. 10 (2019): 930. http://dx.doi.org/10.3390/e21100930.

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The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. The Walsh functions are based on a 2 k × 2 k Hadamard matrix. For general k (= 1 , 2 , ⋯ ), we will prove that 2 k - 1 Walsh functions can generate essentially different balanced and i.i.d. binary sequences that are orthogonal to each other.

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Alghamdi, Mohammed A., and M. Mursaleen. "Hankel matrix transformation of the Walsh–Fourier series." Applied Mathematics and Computation 224 (November 2013): 278–82. http://dx.doi.org/10.1016/j.amc.2013.08.075.

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6

Adi, Prajanto Wahyu, Adi Wibowo, Guruh Aryotejo, and Ferda Ernawan. "Fragile watermarking for image authentication using dyadic walsh ordering." International Journal of Advances in Intelligent Informatics 9, no. 3 (2023): 490. http://dx.doi.org/10.26555/ijain.v9i3.1017.

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A digital image is subjected to the most manipulation. This is driven by the easy manipulating process through image editing software which is growing rapidly. These problems can be solved through the watermarking model as an active authentication system for the image. One of the most popular methods is Singular Value Decomposition (SVD) which has good imperceptibility and detection capabilities. Nevertheless, SVD has high complexity and can only utilize one singular matrix S, and ignore two orthogonal matrices. This paper proposes the use of the Walsh matrix with dyadic ordering to generate a

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Samanta, Supriti, Goutam K. Maity, and Subhadipta Mukhopadhyay. "Implementation of Orthogonal Codes Using MZI." Micro and Nanosystems 12, no. 3 (2020): 159–67. http://dx.doi.org/10.2174/1876402912666200211121624.

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Background: In Code Division Multiple Access (CDMA)/Multi-Carrier CDMA (MCCDMA), Walsh-Hadamard codes are widely used for its orthogonal characteristics, and hence, it leads to good contextual connection property. These orthogonal codes are important because of their various significant applications. Objective: To use the Mach–Zehnder Interferometer (MZI) for all-optical Walsh-Hadamard codes is implemented in this present paper. Method: The Mach–Zehnder Interferometer (MZI) is considered for the Tree architecture of Semiconductor Optical Amplifier (SOA). The second-ordered Hadamard and the inv

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Alotaibi, Abdullah, and M. Mursaleen. "Applications of Hankel and Regular Matrices in Fourier Series." Abstract and Applied Analysis 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/947492.

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Recently, Alghamdi and Mursaleen (2013) used the Hankel matrix to determine the necessary and suffcient condition to find the sum of the Walsh-Fourier series. In this paper, we propose to use the Hankel matrix as well as any general nonnegative regular matrix to obtain the necessary and sufficient conditions to sum the derived Fourier series and conjugate Fourier series.

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Au-Yeung, Enrico. "Sparse reconstruction with multiple Walsh matrices." Advances in Pure and Applied Mathematics 10, no. 3 (2019): 221–39. http://dx.doi.org/10.1515/apam-2017-0047.

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Abstract The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much lower-dimensional vector space. This is the setting of compressed sensing, where the projection is given by a matrix with many more columns than rows. We introduce a class of random matrices that can be used to reconstruct sparse vectors in this paradigm. These matrices satisfy the restricted isometry property with overwhelming probability. We also disc

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CHOU, JYH-HORNG, and ING-RONG HORNG. "Simple methods for the shift-transformation matrix, direct-product matrix and summation matrix of discrete Walsh series." International Journal of Control 43, no. 4 (1986): 1339–42. http://dx.doi.org/10.1080/00207178608933542.

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Gorgadze, S. F., Dao Vu Shi та A. V. Ermakova. "Synchronization of M-sequences based on fast Нadamard transform". Radiotehnika i èlektronika 69, № 2 (2024): 122–36. http://dx.doi.org/10.31857/s0033849424020031.

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Options have been developed for constructing circulant matrices of any M-sequence (MS) based on automorphic multiplicative groups of the extended Galois field, constructed using an irreducible primitive polynomial, on the basis of which the original MS is formed. The result of this approach is the identification of new methods for transforming MS circulant matrices to a matrix of Walsh functions, ordered by the powers of the antiderivative element of the field. It is shown for the first time that, depending on the initial conditions of the transformation, a set of any number of any cyclic shif

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Ebregbe, David, and Wei Bo Deng. "Orthogonal Binary Waveform Optimization for Mimo Radar Systems." Applied Mechanics and Materials 239-240 (December 2012): 376–81. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.376.

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Waveform optimization for multiple-input multiple-output (MIMO) radar systems for good autocorrelation and crosscorrelation properties based on the direct design of the set of orthogonal transmitted time series is considered. Exploiting the orthogonality of non identical walsh functions, which have been used successfully in spread spectrum communication, the Walsh-Hadamard matrix is used as the orthogonal binary signal set followed by the simulated annealing statistical optimization tool to provide an optimal orthogonal binary signal set with the desired correlation properties

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Blahota, István. "Approximation of double Walsh–Fourier series by means of the matrix transform." Ukrains’kyi Matematychnyi Zhurnal 76, no. 5 (2024): 664–79. http://dx.doi.org/10.3842/umzh.v76i5.7397.

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Anderyance, S., and M. Hadizadeh. "THE COMPUTATIONAL EFFICIENCY OF WALSH APPROXIMATION FOR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS." Asian-European Journal of Mathematics 04, no. 02 (2011): 263–70. http://dx.doi.org/10.1142/s1793557111000204.

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In this research, we give details of a new numerical method for the approximate solution of a general two-dimensional Volterra integral equation, using the discontinuous wavelet packets e.g. Walsh functions. The double Walsh approximation we have adopted utilizes a simple robust numerical scheme for approximate solution of the equations. The two-dimensional operational matrix of integration for each subinterval [Formula: see text] is explicitly constructed, where m is a power of 2. Finally the reliability and efficiency of the proposed scheme are demonstrated by some numerical results.

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Sajjad, R. Abdulridh, and S. Hasan Fadhil. "Enhanced SLM based OFDM-DCSK communication system for PAPR reduction." Bulletin of Electrical Engineering and Informatics 11, no. 1 (2022): 567–74. https://doi.org/10.5281/zenodo.6651531.

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In this research, a selective mapping (SLM) technique using the Walsh Hadamard (WH) matrix, the Riemann matrix, and the new enhanced Riemann matrix were introduced to reduce the peak to average power ratio (PAPR) of orthogonal frequency division multiplexing based differential chaos shift keying (OFDM-DCSK). Using a new algorithm to reduce the size of the Riemann matrix, which in turn enhances the computational complexity of the SLM system without affecting the performance of PAPR in the main method. The simulation results show that the SLM technique using the Riemann matrix gives better PAPR

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LI, Yu, He-xin CHEN, Ai-jun SANG, and Hua FENG. "Four-dimensional matrix Walsh transform for lossless compression of color video." Journal of China Universities of Posts and Telecommunications 17, no. 3 (2010): 123–28. http://dx.doi.org/10.1016/s1005-8885(09)60461-1.

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17

Save, Jagruti Ketan. "Walsh Transform based Feature vector generation for Image Database Classification." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (2016): 1176. http://dx.doi.org/10.11591/ijece.v6i3.8922.

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Thousands of images are generated everyday, which implies the need to build an easy, faster, automated classifier to classify and organize these images. Classification means selecting an appropriate class for a given image from a set of pre-defined classes. The main objective of this work is to explore feature vector generation using Walsh transform for classification. In the first method, we applied Walsh transform on the columns of an image to generate feature vectors. In second method, Walsh wavelet matrix is used for feature vector generation. In third method we proposed to apply vector qu

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Save, Jagruti Ketan. "Walsh Transform based Feature vector generation for Image Database Classification." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (2016): 1176. http://dx.doi.org/10.11591/ijece.v6i3.pp1176-1182.

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Thousands of images are generated everyday, which implies the need to build an easy, faster, automated classifier to classify and organize these images. Classification means selecting an appropriate class for a given image from a set of pre-defined classes. The main objective of this work is to explore feature vector generation using Walsh transform for classification. In the first method, we applied Walsh transform on the columns of an image to generate feature vectors. In second method, Walsh wavelet matrix is used for feature vector generation. In third method we proposed to apply vector qu

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Nayak, Dibyalekha, Kananbala Ray, Tejaswini Kar, and Chiman Kwan. "Walsh–Hadamard Kernel Feature-Based Image Compression Using DCT with Bi-Level Quantization." Computers 11, no. 7 (2022): 110. http://dx.doi.org/10.3390/computers11070110.

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To meet the high bit rate requirements in many multimedia applications, a lossy image compression algorithm based on Walsh–Hadamard kernel-based feature extraction, discrete cosine transform (DCT), and bi-level quantization is proposed in this paper. The selection of the quantization matrix of the block is made based on a weighted combination of the block feature strength (BFS) of the block extracted by projecting the selected Walsh–Hadamard basis kernels on an image block. The BFS is compared with an automatically generated threshold for applying the specific quantization matrix for compressi

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Zhou, Zhong, Jiangfeng Hu, Fan Li, Junjie Zhang, and Mingfeng Lei. "Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula." Applied Sciences 12, no. 10 (2022): 5142. http://dx.doi.org/10.3390/app12105142.

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Foamed concrete consists of cement matrix and air-foam and has more complicated structure characteristics than normal concrete. However, current research on the elastic modulus of foamed concrete is still limited to empirical equations. In this work, a new theoretical prediction model was proposed for calculating the elastic modulus of foamed concrete. The elastic modulus calculation model for the spherical shell element of foamed concrete is constructed based on the Walsh formula and the assumption of spherical pores. Moreover, the theoretical prediction model is established by introducing th

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21

Bouyukliev, Iliya, Mariya Dzhumalieva-Stoeva, and Paskal Piperkov. "Matrix Factorization and Some Fast Discrete Transforms." Axioms 13, no. 8 (2024): 495. http://dx.doi.org/10.3390/axioms13080495.

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In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered

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Marti-Puig, P. "A Family of Fast Walsh Hadamard Algorithms With Identical Sparse Matrix Factorization." IEEE Signal Processing Letters 13, no. 11 (2006): 672–75. http://dx.doi.org/10.1109/lsp.2006.879472.

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23

Selvaraj, Chikkanna R., and Suguna Selvaraj. "Matrix Transformations and Disk of Convergence in Interpolation Processes." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–11. http://dx.doi.org/10.1155/2008/905635.

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Let denote the set of functions analytic in but not on . Walsh proved that the difference of the Lagrange polynomial interpolant of and the partial sum of the Taylor polynomial of converges to zero on a larger set than the domain of definition of . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and Hermite-Birkhoff interpolation processes in a similar manner. In this paper, we apply a certain matrix transformation on the sequences of operators given in the above-mentioned interpolation processes to prove the convergence in larger disks.

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24

Laikova, L. G., T. A. Tereshchenko, and Y. S. Yamnenko. "Matrix calculation of correlation characteristics based on spectral methods." Технология и конструирование в электронной аппаратуре, no. 3-4 (2020): 11–16. http://dx.doi.org/10.15222/tkea2020.3-4.11.

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The paper is devoted to the problem of calculation of autocorrelation function that is important for solving the tasks that require finding the repeating intervals of the signal or defining the main frequency of the signal against the background of non-stationary noise. The authors propose an algorithm to transform the connection between arithmetic and logical correlation functions in oriented basis into the matrix form. Comparative analysis is conducted for the computational complexity of different types of autocorrelation functions using different spectral methods — Fourier, Walsh, and orien

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Klen, Kateryna, Vadym Martynyuk, and Mykhailo Yaremenko. "Prediction of the wind speed change function by linear regression method." Computational Problems of Electrical Engineering 9, no. 2 (2019): 28–33. http://dx.doi.org/10.23939/jcpee2019.02.028.

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In the article the approximation of the function of wind speed changes by linear functions based on Walsh functions and the prediction of function values by linear regression method is made. It is shown that under the condition of a linear change of the internal resistance of the wind generator over time, it is advisable to introduce the wind speed change function with linear approximation. The system of orthonormal linear functions based on Walsh functions is given. As an example, the approximation of the linear-increasing function with a system of 4, 8 and 16 linear functions based on the Wa

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Blahota, István, and György Gát. "Norm and almost everywhere convergence of matrix transform means of Walsh-Fourier series." Acta Universitatis Sapientiae, Mathematica 15, no. 2 (2023): 244–58. http://dx.doi.org/10.2478/ausm-2023-0013.

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Abstract We show the uniformly boundedness of the L1 norm of general matrix transform kernel functions with respect to the Walsh-Paley system. Special such matrix means are the well-known Cesàro, Riesz, Bohner-Riesz means. Under some conditions, we verify that the kernels K n T = ∑ k = 1 n t k , n D k {\rm{K}}_{\rm{n}}^{\rm{T}} = \sum\nolimits_{{\rm{k = 1}}}^{\rm{n}} {{{\rm{t}}_{{\rm{k}},{\rm{n}}}}{{\rm{D}}_{\rm{k}}}} , (where Dk is the kth Dirichlet kernel) satisfy ‖ K n T ‖ 1 ≤ c . {\left\| {{\rm{K}}_{\rm{n}}^{\rm{T}}} \right\|_1} \le {\rm{c}}{\rm{.}} As a result of this we prove that for an

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FUJII, KAZUYUKI, KUNIO FUNAHASHI, and TAKAYUKI KOBAYASHI. "JARLSKOG'S PARAMETRIZATION OF UNITARY MATRICES AND QUDIT THEORY." International Journal of Geometric Methods in Modern Physics 03, no. 02 (2006): 269–83. http://dx.doi.org/10.1142/s0219887806001144.

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In the paper (math–ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie group theory (math–ph/0505047). In this paper we apply the method to a quantum computation based on multilevel system (qudit theory). Namely, by considering that the parametrization gives a complete set of modules in qudit theory, we construct the generalized Pauli matrices, which play a central role in the theory and also make a comment on the exchange gate of two–qudit systems. Moreover, we give an explicit constr

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Saito, Naoki, and Yiqun Shao. "eGHWT: The Extended Generalized Haar–Walsh Transform." Journal of Mathematical Imaging and Vision 64, no. 3 (2022): 261–83. http://dx.doi.org/10.1007/s10851-021-01064-w.

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AbstractExtending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important, and much research has been done recently. The generalized Haar–Walsh transform (GHWT) developed by Irion and Saito (2014) is a multiscale transform for signals on graphs, which is a generalization of the classical Haar and Walsh–Hadamard transforms. We propose the extended generalized Haar–Walsh transform (eGHWT), which is a generalization of the adapted time–frequency tilings of Thiele and Villemoes (1996). The eGHWT exami

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29

K, Swaraja, Meenakshi K, Ushakumari Ch, and Kishore D. "A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution." F1000Research 11 (November 16, 2022): 1333. http://dx.doi.org/10.12688/f1000research.124720.1.

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\textit{Background} The proposed watermarking framework is based on the multi-resolution Walsh-Hadamard Transform (MR-WHT) along with Schur factorization. For embedding, the cover image is converted into a frequency domain using MR-WHT before Schur factorization is applied. \textit{Methods} The upper triangle's highest stable eigenvalues in the Schur factorization are employed as reliable embedding locations for the watermark. The singular values of these coefficients are updated with the singular values of the watermark, and the matrix array generated by the biggest eigenvalues is further fac

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Abdulridha, Sajjad R., and Fadhil S. Hasan. "Enhanced SLM based OFDM-DCSK communication system for PAPR reduction." Bulletin of Electrical Engineering and Informatics 11, no. 1 (2022): 567–74. http://dx.doi.org/10.11591/eei.v11i1.3549.

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In this research, a selective mapping (SLM) technique using the Walsh Hadamard (WH) matrix, the Riemann matrix, and the new enhanced Riemann matrix were introduced to reduce the peak to average power ratio (PAPR) of orthogonal frequency division multiplexing based differential chaos shift keying (OFDM-DCSK). Using a new algorithm to reduce the size of the Riemann matrix, which in turn enhances the computational complexity of the SLM system without affecting the performance of PAPR in the main method. The simulation results show that the SLM technique using the Riemann matrix gives better PAPR

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31

Corcoran, Timothy C. "Compressive Detection of Highly Overlapped Spectra Using Walsh–Hadamard-Based Filter Functions." Applied Spectroscopy 72, no. 3 (2017): 392–403. http://dx.doi.org/10.1177/0003702817738023.

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In the chemometric context in which spectral loadings of the analytes are already known, spectral filter functions may be constructed which allow the scores of mixtures of analytes to be determined in on-the-fly fashion directly, by applying a compressive detection strategy. Rather than collecting the entire spectrum over the relevant region for the mixture, a filter function may be applied within the spectrometer itself so that only the scores are recorded. Consequently, compressive detection shrinks data sets tremendously. The Walsh functions, the binary basis used in Walsh–Hadamard transfor

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MIYAGAWA, Isao, and Yukinobu TANIGUCHI. "Dense Light Transport for Relighting Computation Using Orthogonal Illumination Based on Walsh-Hadamard Matrix." IEICE Transactions on Information and Systems E99.D, no. 4 (2016): 1038–51. http://dx.doi.org/10.1587/transinf.2015cyp0002.

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Liu, Li Zhao, Yu Feng Chen, Tian Hua Zhang, Ying Wang, and Mao Qing Li. "Design and Implementation of Maxi-Linear Deviation Search Algorithm Based on Improved ICP." Advanced Materials Research 143-144 (October 2010): 293–97. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.293.

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To solve the problem of calculating the maximum linear deviation in block cipher algorithm linear analysis, the paper has proposed a search method and improved algorithm based on iterative closest point (ICP) of the maximum deviation. The ciphertext and its coefficient matrix is initialized as range image matrix, using ICP algorithm to calculate the best match state of adjacent range image, and the linear deviation value of round function transformation of this time was proved to be the maximum linear deviation by applying generalized Walsh spectrum; by proposing the initial rule corresponding

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Patil, Rita B. "Performance Analysis of Walsh-Hadamard Transform-Based Gabor Filter Feature Extraction Method and GLCM Feature Extraction Method for Brain Tumor Detection." International Journal for Research in Applied Science and Engineering Technology 12, no. 7 (2024): 220–23. http://dx.doi.org/10.22214/ijraset.2024.63543.

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Abstract: Brain tumor detection through MRI imaging is a crucial step in medical diagnostics. This paper presents a comparative performance analysis of two feature extraction methods: the Walsh-Hadamard Transform (WHT) based Gabor Filter method and the Gray-Level Co-occurrence Matrix (GLCM) method. We evaluate these techniques based on accuracy, computational efficiency, and robustness using a benchmark MRI dataset. Our results indicate the strengths and limitations of each method, providing insights for their application in automated brain tumor detection systems.

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Grigoriev, E. "Spectral Characteristics Analysis of Images Matrix Masking Results." Proceedings of Telecommunication Universities 10, no. 2 (2024): 76–82. http://dx.doi.org/10.31854/1813-324x-2024-10-2-76-82.

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The article describes the results of a computational experiment to assess the capabilities of extracting useful information if an image masked by quasi-orthogonal matrices sent over an open channel became available to a third party. Hadamard and Mersenne matrices of symmetric and cyclic structure are considered. The results confirm the data that images masked by small-sized matrix leaves edges of the original image on the masked image. However, with an increase in the size of the masking matrix, all considered in the article matrices reliably hides the original image during visual analysis. Ma

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Blahota, István. "Approximation by de la Vallée Poussin type Marcinkiewicz matrix transform means of Walsh-Fourier series." Mathematical Inequalities & Applications, no. 3 (2024): 529–48. http://dx.doi.org/10.7153/mia-2024-27-36.

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Vose, Michael D., and Alden H. Wright. "The Simple Genetic Algorithm and the Walsh Transform: Part I, Theory." Evolutionary Computation 6, no. 3 (1998): 253–73. http://dx.doi.org/10.1162/evco.1998.6.3.253.

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This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite populat

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Denisov, А., Y. Denisov, O. Bursala, and O. Bursala. "CONTROL OF WORKING BODY OF AIRBORNE AIRCRAFT POSITIONING MECHANISMS BY MEANS OF STEPPER MOTOR IN STEP CRUSHING MODE." Наукові праці Державного науково-дослідного інституту випробувань і сертифікації озброєння та військової техніки, no. 12 (July 5, 2022): 41–52. http://dx.doi.org/10.37701/dndivsovt.12.2022.05.

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Step splitting control mode of the electric drives stepper motors working bodies of the positioning mechanisms of onboard aviation equipment is carried out by means of programmable controllers. From their output signals, pulse-wide signals are formed by means of drivers that control power transistors, which are included in the windings of a stepper motor. A simpler version of building control systems for stepper motors (SM) involves the use of programmable timers, which requires its reprogramming when changing the step splitting factor. In the process of step splitting the shape of

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Blahota, István. "Approximation by a special de la Vallée Poussin type matrix transform mean of Walsh-Fourier series." Miskolc Mathematical Notes 24, no. 3 (2023): 1213. http://dx.doi.org/10.18514/mmn.2023.4249.

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40

Faure, Andre J., Ben Lehner, Verónica Miró Pina, Claudia Serrano Colome, and Donate Weghorn. "An extension of the Walsh-Hadamard transform to calculate and model epistasis in genetic landscapes of arbitrary shape and complexity." PLOS Computational Biology 20, no. 5 (2024): e1012132. http://dx.doi.org/10.1371/journal.pcbi.1012132.

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Accurate models describing the relationship between genotype and phenotype are necessary in order to understand and predict how mutations to biological sequences affect the fitness and evolution of living organisms. The apparent abundance of epistasis (genetic interactions), both between and within genes, complicates this task and how to build mechanistic models that incorporate epistatic coefficients (genetic interaction terms) is an open question. The Walsh-Hadamard transform represents a rigorous computational framework for calculating and modeling epistatic interactions at the level of ind

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Pashinska-Gadzheva, Maria, and Iliya Bouyukliev. "About Algorithms for Calculation of Covering Radius of Linear Codes." Innovative STEM Education 6, no. 1 (2024): 95–98. https://doi.org/10.55630/stem.2024.0609.

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The covering radius is an important parameter of linear codes. Its calculation is an NP-complete problem. There are three main approaches to its computing that can be considered. The first method is based on traversing the cosets of the linear code. The second method uses the parity-check matrix of the code to calculate the covering radius. The third method is based on fast Walsh-Hadamard transforms for the binary case and Vilenkin-Chrestenson transform for the non-binary case. In this work, the first two approaches are considered and some of the features of their implementations are presented

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Bykov, V. N., G. Yu Miroshnik, and T. V. Miroshnik. "Evaluation of accuracy of radiometric correlation-extreme navigation systems." 34, no. 34 (June 30, 2021): 7–13. http://dx.doi.org/10.26565/2311-0872-2021-34-01.

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Background: The use of passive matrix radiometric sensors of the millimeter wave range in aircraft navigation systems, which make it possible to form a radiometric image of a ground navigation object under conditions of high-speed flight of aircraft, is one of the effective ways to ensure high accuracy in measuring the coordinates of objects and, ultimately, leads to an increase in the probability of positioning aircraft [1]. In work [2], analytical relationships were obtained and quantitative estimates of the accuracy of positioning of aircraft equipped with a matrix radiometric navigation sy

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Grigoriev, E., and A. Sergeev. "Quality Analysis of Matrix Masking of Digital Audio Data." Proceedings of Telecommunication Universities 9, no. 3 (2023): 6–13. http://dx.doi.org/10.31854/1813-324x-2023-9-3-6-13.

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This article considered the guarantee of confidentiality task of audio information transmitted over a packet communication channel. Domain analysis showed, that in most cases cryptographical method used for guarantee of confidentiality of audio information, however, along with them, matrix methods of protective coding used, with implementation on FPGA or DSP processors. These methods, using random matrices, impose additional instrumental errors during decoding. The purpose of the study: is to assess the quality of protective coding ‒ masking of audio data by quasi-orthogonal structured matrice

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LEE, HAIYOUNG, and ZEUNGNAM BIEN. "Method of computing the inverse of a matrix whose elements are a linear combination of Walsh functions." International Journal of Control 47, no. 5 (1988): 1235–42. http://dx.doi.org/10.1080/00207178808906091.

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JIANG, Z. H. "New method for computing the inverse of a matrix whose elements are linear combinations of Walsh functions." International Journal of Systems Science 20, no. 11 (1989): 2335–40. http://dx.doi.org/10.1080/00207728908910311.

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Tohidi, Emran, F. Soleymani, and Adem Kilicman. "Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/535979.

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The idea of approximation by monomials together with the collocation technique over a uniform mesh for solvingstate-space analysisandoptimal controlproblems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of

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Gonzalez-Conde, Javier, Thomas W. Watts, Pablo Rodriguez-Grasa, and Mikel Sanz. "Efficient quantum amplitude encoding of polynomial functions." Quantum 8 (March 21, 2024): 1297. http://dx.doi.org/10.22331/q-2024-03-21-1297.

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Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for the application of these algorithms. Here, we present and compare two efficient methods for the amplitude encoding of real polynomial functions on n qubits. This case holds special relevance, as any continuous function on a closed interval can be uniformly approximated with arbitrary precision by a polynomial function. The first approach relies on the matrix product

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WANG, Yulong, and Ji REN. "WHIT: A More Efficient Hybrid Method for Single-Packet IP Traceback Using Walsh Matrix and Router Degree Distribution." IEICE Transactions on Communications E96.B, no. 7 (2013): 1896–907. http://dx.doi.org/10.1587/transcom.e96.b.1896.

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Zinde-Walsh, Victoria. "Errata." Econometric Theory 6, no. 2 (1990): 293. http://dx.doi.org/10.1017/s0266466600005259.

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There are some errors in the paper by Victoria Zinde-Walsh, “Some Exact Formulae for Autoregressive Moving Average Processes,” Econometric Theory 4 (1988): 384–402. The following is a list of corrections.On page 393 the τ * τ matrices El,E2 should be replaced by their transposes ,, respectively, throughout. In (3.21) the expression (S3 – λλA3) should be replaced by (S3 – λλA3) in the definitions of both T1, and T3. In (3.8), (3.21), (5.1), and (5.2) the entry in the bottom right-hand corner should be pre- and post-multiplied by λ. In (3.6) the matrix is obtained as the negative of the matrix d

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Dziech, Andrzej. "New Orthogonal Transforms for Signal and Image Processing." Applied Sciences 11, no. 16 (2021): 7433. http://dx.doi.org/10.3390/app11167433.

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In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having

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