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Journal articles on the topic 'Wavelet coefficients'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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1

DEBNATH, LOKENATH, and SARALEES NADARAJAH. "POPULAR WAVELET MODELS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (2007): 655–66. http://dx.doi.org/10.1142/s0219691307001951.

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The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for two popular models for the marginal posterior density. We also illustrate the superior performance of these models over the standard models for wavelet coefficients.

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LEWALLE, JACQUES. "FIELD RECONSTRUCTION FROM SINGLE SCALE CONTINUOUS WAVELET COEFFICIENTS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (2009): 131–42. http://dx.doi.org/10.1142/s0219691309002738.

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The redundancy of continuous wavelet transforms implies that the wavelet coefficients are not independent of each other. This interdependence allows the reconstruction or approximation of the wavelet transform, and of the original field, from a subset of the wavelet coefficients. Contrasting with lines of modulus maxima, known to provide useful partition functions and some data compaction, the reconstruction from single-scale coefficients is derived for the Hermitian family of wavelets. The formula is exact in the continuum for d-dimensional fields, and its limitations under discretization are

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Liu, Chenhua, and Anhong Wang. "State-Aware High-Order Diffusion Method for Edge Detection in the Wavelet Domain." Symmetry 15, no. 4 (2023): 803. http://dx.doi.org/10.3390/sym15040803.

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This paper addresses how to use high-order diffusion to restore the wavelet coefficients in the wavelet domain. To avoid image distortion, wavelets with symmetry are used for image decomposition to obtain the wavelet coefficients of each sub-band. Due to the influence of noise, it is particularly important to obtain the wavelet coefficients, which can accurately reflect the image information. According to the characteristics of wavelet threshold shrinkage and the advantages of the high-order variational method in denoising, a wavelet coefficient restoration scheme is proposed. The theoretical

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Jiang, Tian Hua, and Jing Rong Peng. "Digital Simulation of Bridge Wind Fields Based on Wavelet Method." Advanced Materials Research 201-203 (February 2011): 2532–35. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.2532.

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Digital simulation of stochastic wind velocity field is prerequisite to flutter or buffeting analysis of long-span bridges in time-domain. Wavelet method was applied to the simulation of the stochastic wind field, performing the effective simulation of spatial stochastic wind field. According to the idea of multi-resolution analysis and orthonormal wavelets, relationship between wavelet coefficients and PSD(power spectral density)function is deduced , then the wavelet coefficients on each and every scale are obtained from the given PSD function, the intermittency was introduced into wavelet co

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5

Cattani, Carlo. "Shannon Wavelets Theory." Mathematical Problems in Engineering 2008 (2008): 1–24. http://dx.doi.org/10.1155/2008/164808.

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Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets areC∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeom

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Jansen, Maarten. "Non-equispaced B-spline wavelets." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (2016): 1650056. http://dx.doi.org/10.1142/s0219691316500569.

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This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen–Daubechies–Feauveau wavelets. The new construction is based on the factorization of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the f

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Yin, Ming, Wei Liu, Jun Shui, and Jiangmin Wu. "Quaternion Wavelet Analysis and Application in Image Denoising." Mathematical Problems in Engineering 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/493976.

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The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatialL2(R2), proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale spaceL2(R2;H), and studies quaternion wavelet transform structure. Finally, the quaternion wavelet transform is applied to image denoising, and generalized Gauss distribution is used to model QWT coefficients’ magnitude distribution, under the Bayesian theory framework, to re

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Zhou, Guang-Dong, You-Liang Ding, and Ai-Qun Li. "Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/870420.

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Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typh

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Shumilov, Boris M. "An Algorithm with the Even-odd Splitting of the Wavelet Transform of Non-Hermitian Splines of the Seventh Degree." WSEAS TRANSACTIONS ON SIGNAL PROCESSING 18 (March 2, 2022): 25–36. http://dx.doi.org/10.37394/232014.2022.18.4.

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The article investigates an implicit method of decomposition of the 7th degree non-Hermitian splines into a series of wavelets with two zero moments. The system of linear algebraic equations connecting the coefficients of the spline expansion on the initial scale with the spline coefficients and wavelet coefficients on the embedded scale is obtained. The even-odd splitting of the wavelet decomposition algorithm into a solution of the half-size five-diagonal system of linear equations and some local averaging formulas are substantiated. The results of numerical experiments on accuracy on polyno

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Ghasemi-Ghalebahman, Ahmad, Mohammad-Reza Ashory, and Mohammad-Javad Kokabi. "A proper lifting scheme wavelet transform for vibration-based damage identification in composite laminates." Journal of Thermoplastic Composite Materials 31, no. 5 (2017): 668–88. http://dx.doi.org/10.1177/0892705717718239.

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Damage detection using the wavelet transform was investigated and appropriate approaches to raising the method’s sensitivity level were proposed. In addition, the current study attempted to implement the impulse wavelet design algorithm in order to present appropriate wavelet function with respect to the characteristics of the signal. The initial wavelet function corresponding to the impulse response of composite plate was achieved using impulse wavelet algorithm in time domain. The function was optimized using lifting scheme method. To detect damages, an appropriate signal was selected throug

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Cattani, Carlo, and Aleksey Kudreyko. "Application of Periodized Harmonic Wavelets towards Solution of Eigenvalue Problems for Integral Equations." Mathematical Problems in Engineering 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/570136.

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This article deals with the application of the periodized harmonic wavelets for solution of integral equations and eigenvalue problems. The solution is searched as a series of products of wavelet coefficients and wavelets. The absolute error for a general case of the wavelet approximation was analytically estimated.

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Dahraoui, Nadia, M'hamed Boulakroune, S. Khelfaoui, S. Kherroubi, and Yamina Benkrima. "Effectiveness of Wavelet Denoising on Secondary Ion Mass Spectrometry Signals." East European Journal of Physics, no. 3 (September 4, 2023): 495–500. http://dx.doi.org/10.26565/2312-4334-2023-3-56.

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Wavelet theory has already achieved huge success. For Secondary Ions Mass Spectrometry (SIMS) signals, denoising the secondary signal, which is altered by the measurement, is considered that an essential step prior to applying such a signal processing technique that aims enhance the SIMS signals.The most efficient and widely used wavelet denoising method is based on wavelet coefficient thresholding. This process involves three important steps; wavelet decomposition: the input signals are decomposed into wavelet coefficients, thresholding: the wavelet coefficients are modified according to a th

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Abdullah, Shahrum, S. N. Sahadan, Mohd Zaki Nuawi, and Zulkifli Mohd Nopiah. "Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform." Key Engineering Materials 462-463 (January 2011): 461–66. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.461.

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The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DW

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MAHARAJ, ELIZABETH ANN. "USING WAVELETS TO COMPARE TIME SERIES PATTERNS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 04 (2005): 511–21. http://dx.doi.org/10.1142/s0219691305000993.

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In this paper, a procedure for comparing the patterns of time series using wavelets is developed. Randomization tests based on the ratio of the sum of squared wavelet coefficients of pairs of time series at different scales are used. A simulation study using pairs of different types of time series using the Haar and Daubechies wavelets is carried out. The results reveal that the tests perform fairly well at scales where there are a sufficient number of wavelet coefficients. The tests are applied to a set of financial time series.

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KUMARI, R. SHANTHA SELVA, S. BHARATHI, and V. SADASIVAM. "QRS COMPLEX DETECTION USING OPTIMAL DISCRETE WAVELET." International Journal of Computational Intelligence and Applications 08, no. 02 (2009): 97–109. http://dx.doi.org/10.1142/s1469026809002576.

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Wavelet transform has emerged as a powerful tool for time frequency analysis of complex nonstationary signals such as the electrocardiogram (ECG) signal. In this paper, the design of good wavelets for cardiac signal is discussed from the perspective of orthogonal filter banks. Optimum wavelet for ECG signal is designed and evaluated based on perfect reconstruction conditions and QRS complex detection. The performance is evaluated by using the ECG records from the MIT-BIH arrhythmia database. In the first step, the filter coefficients (optimum wavelet) is designed by reparametrization of filter

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Tkacheshak, N. V., and М. І. Horbiichuk. "INVESTIGATION OF EXHAUSTING PHENOMENA OF GAS TURBINE ENGINE ON THE BASIS OF WAVELET ANALYSIS." Scientific Bulletin of Ivano-Frankivsk National Technical University of Oil and Gas, no. 2(45) (November 27, 2018): 24–33. http://dx.doi.org/10.31471/1993-9965-2018-2(45)-24-33.

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The method for research of a gas turbine engine (GTE) surging phenomena based on wavelet analysis was developed. GTE DG-90 was chosen for research. A wavelet decomposition of the air pressure signal was carried out using a high pressure compressor and Dobeski, Symlet, Coffle and Meyer's discrete wavelet. The advantages and disadvantages of filtering properties of these wavelets were graphically represented in the form of amplitude-frequency characteristics. Based on the results obtained, a wavelet transform parameter selection scheme based on the analysis of the frequency response of wavelet f

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Ahmadi, H., G. Dumont, F. Sassani, and R. Tafreshi. "Performance of Informative Wavelets for Classification and Diagnosis of Machine Faults." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 03 (2003): 275–89. http://dx.doi.org/10.1142/s0219691303000189.

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This paper deals with an application of wavelets for feature extraction and classification of machine faults in a real-world machine data analysis environment. We have utilized informative wavelet algorithm to generate wavelets and subsequent coefficients that are used as feature variables for classification and diagnosis of machine faults. Informative wavelets are classes of functions generated from a given analyzing wavelet in a wavelet packet decomposition structure in which for the selection of best wavelets, concepts from information theory, i.e. mutual information and entropy are utilize

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Cattani, Carlo. "Fractional Calculus and Shannon Wavelet." Mathematical Problems in Engineering 2012 (2012): 1–26. http://dx.doi.org/10.1155/2012/502812.

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An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for anyL2(ℝ)function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

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Zhang, Ming, Zhuo Ma, and Min Xuan Zhang. "FPGA Implementation of Rational Symmetric Biorthogonal 11-9 Wavelet Transform." Applied Mechanics and Materials 182-183 (June 2012): 1791–95. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1791.

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Coefficients of most existing wavelets are irrational, and it costs much hardware resources when implementing on FPGA, which is inefficient especially in embedded system. Some rational wavelets can overcome this deficiency by elaborate design. Motivated by previous works on rational wavelets, we establish a hardware structure for rational 1-D symmetric biorthogonal 11-9 wavelet and implement it on Xilinx FPGA XC3S500E. The experiment reveals that the area in slices of rational 1-D 11-9 wavelet is less than 1/2 of the pipelined 9-7 wavelet when implementing on FPGA.

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Jayanthi, S., and C. R. Rene Robin. "Analysis of Microarray Data by Empirical Wavelet Transform for Cancer Classification Using Block by Block Method." Journal of Medical Imaging and Health Informatics 11, no. 3 (2021): 697–702. http://dx.doi.org/10.1166/jmihi.2021.3318.

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In this study, DNA microarray data is analyzed from a signal processing perspective for cancer classification. An adaptive wavelet transform named Empirical Wavelet Transform (EWT) is analyzed using block-by-block procedure to characterize microarray data. The EWT wavelet basis depends on the input data rather predetermined like in conventional wavelets. Thus, EWT gives more sparse representations than wavelets. The characterization of microarray data is made by block-by-block procedure with predefined block sizes in powers of 2 that starts from 128 to 2048. After characterization, a statistic

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Cattani, Carlo. "Shannon Wavelets for the Solution of Integrodifferential Equations." Mathematical Problems in Engineering 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/408418.

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Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. Shannon wavelets areC∞-functions and their any order derivatives can be

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ZHU, XIU-GE, BAO-BIN LI, and DENG-FENG LI. "ORTHOGONAL WAVELET TRANSFORM OF SIGNAL BASED ON COMPLEX B-SPLINE BASES." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 06 (2012): 1250054. http://dx.doi.org/10.1142/s0219691312500543.

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In this paper, an orthogonal wavelet transform of signal based on complex B-spline bases is given. The new wavelet transform realizes accurate computation of coefficients of complex B-spline base functions. It integrates good properties of orthogonality, symmetry and continuity, and offers better approximations to continuous signal than do the Haar wavelet and Daubechies wavelets. All algorithms of the new orthogonal wavelet transform are based on explicit formulas and easy to be implemented.

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Kuznetsov, Nikolay A. "METHOD FOR CONSTRUCTING NONLINEAR WAVELET CODE TO ENSURE DATA INTEGRITY IN COMMUNICATION CHANNELS." T-Comm 15, no. 2 (2021): 26–32. http://dx.doi.org/10.36724/2072-8735-2021-15-2-26-32.

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A method for constructing a nonlinear wavelet code (NVC) to ensure data integrity in communication channels, taking into account current threats to information security in a modern dynamic stochastic environment, is proposed. A special place among the methods of combating threats to the integrity of information is occupied by noise-resistant encoding. The article presents a computationally effective method for ensuring data integrity in communication channels by using nonlinear transformations and wavelets. The approximation of the wavelet transform refers to the division of the signal into ap

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Guariglia, Emanuel, and Rodrigo Capobianco Guido. "Chebyshev Wavelet Analysis." Journal of Function Spaces 2022 (June 30, 2022): 1–17. http://dx.doi.org/10.1155/2022/5542054.

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This paper deals with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due to the connection coefficients. Uniform convergence of Chebyshev wavelets and their approximation error allow us to provide rigorous proofs. In particular, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. Finally, we give two examples concerning the main properties proved.

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Mathew, K., and S. Shibu. "Reconstruction of Wavelet Coefficients." International Journal of Computer Applications 97, no. 15 (2014): 27–34. http://dx.doi.org/10.5120/17086-7542.

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Song, Yu Yang, Rong Li, Ming Yan Li, and Wen Hui Zhang. "Relationship between Scale and Period and its Ecological Applications in Wavelet Analysis." Advanced Materials Research 726-731 (August 2013): 4252–57. http://dx.doi.org/10.4028/www.scientific.net/amr.726-731.4252.

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The relations between the scales and periods of Mexican Hat (Mexh) and Morlet (Morl) wavelets have been deduced. Based on these relations, variances, coefficients, and power spectra of these two wavelets’ original and eco-used wavelets are compared and analyzed theoretically and experimentally for the distribution pattern of Haloxylon ammodendron Bunge population in Gurban Tonggut desert, China. The research shows that: (1) Mexh and Morl eco-used wavelets can be simultaneously used to describe the distribution period of Haloxylon population and to study the same phenomenon by combining these t

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Ďuriš, Viliam, Sergey G. Chumarov, and Vladimir I. Semenov. "Increasing the Speed of Multiscale Signal Analysis in the Frequency Domain." Electronics 12, no. 3 (2023): 745. http://dx.doi.org/10.3390/electronics12030745.

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In the Mallat algorithm, calculations are performed in the time domain. To speed up the signal conversion at each level, the wavelet coefficients are sequentially halved. This paper presents an algorithm for increasing the speed of multiscale signal analysis using fast Fourier transform. In this algorithm, calculations are performed in the frequency domain, which is why the authors call this algorithm multiscale analysis in the frequency domain. For each level of decomposition, the wavelet coefficients are determined from the signal and can be calculated in parallel, which reduces the conversi

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FAROOQ, OMAR, and SEKHARJIT DATTA. "EVALUATION OF A WAVELET BASED ASR FRONT-END." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (2007): 641–54. http://dx.doi.org/10.1142/s021969130700194x.

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In this paper, we propose the use of the wavelet transform for the extraction of features for phonemes in order to overcome some of the shortcomings of short time Fourier transform. New log-energy based features are proposed using discrete wavelet transform as well as wavelet packets and their recognition performance has been evaluated. These features overcome the problem of shift variance as encountered in the features based on the discrete wavelet transform coefficients. The effect on the recognition performance by choosing different mother wavelets for the decomposition and window duration

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Akimov, Pavel A., and Mojtaba Aslami. "Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam." Applied Mechanics and Materials 580-583 (July 2014): 2924–27. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2924.

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This paper is devoted to correct and efficient method of local static analysis of Bernoulli beam on elastic foundation. First of all, problem discretized by finite difference method, and then transformed to a localized one by using the Haar wavelets. Finally, imposing an optimal reduction in wavelet coefficients, the localized, reduced results can be obtained. It becomes clear after comparison with analytical solutions, that the localization of the problem by multiresolution wavelet approach gives exact solution in desired regions of beam even in high level of reduction in wavelet coefficients

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Umezu, Nobuyuki, and Masatomo Inui. "Lossy Compression of Z-Map Based Shape Models Using Daubechies Wavelet Transform and Quickselect." International Journal of Automation Technology 18, no. 5 (2024): 613–20. http://dx.doi.org/10.20965/ijat.2024.p0613.

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We propose an algorithm for lossy compression of computer-aided design models in Z-map representation. Our method employs Daubechies wavelet functions, which are smoother than those of the Haar wavelet used in a previous work for the lossy compression of shape models. A significant reduction in the amount of data of the compressed shape model was achieved using the proposed lossy in which the least significant coefficients of the wavelet synopsis were deleted. The nonlinear filtering of coefficients was based on the quickselect algorithm, which was seven to ten times faster than a normal quick

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Li, Yan Hui, and Yu Liang Gao. "Wavelet-Based Steganography against Histogram Analysis." Applied Mechanics and Materials 40-41 (November 2010): 469–72. http://dx.doi.org/10.4028/www.scientific.net/amm.40-41.469.

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Histogram analysis for wavelet coefficients is powerful steganalysis for detecting the presence of secret information embedded in the wavelet coefficients. In order to improve the security, a wavelet-based steganography against histogram analysis is presented. First, a cover image is divided into blocks, and every block is decomposed into wavelet. Then, if the secret bit is not same as the information denoted by nonzero wavelet coefficient, the absolute value of wavelet coefficient is subtracted by 1, if the value of wavelet coefficient was 0 after embedding the secret bit, the secret bit shou

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REVATHY, K., G. RAJU, and S. R. PRABHAKARAN NAYAR. "IMAGE ZOOMING BY WAVELETS." Fractals 08, no. 03 (2000): 247–53. http://dx.doi.org/10.1142/s0218348x00000342.

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Enlargement and reduction of images are often required in image processing. Popular methods for re-sizing are standard interpolation methods. Recently, wavelets and fractal-based methods are developed for re-sizing. In this paper, wavelet zooming algorithm based on pyramid algorithm for wavelet transformation is explained. Also performance analysis of wavelet-based zooming method is investigated. We find that wavelet zooming with enhanced coefficients gives better visual quality. The objective error analysis also agrees with this. Wavelet zooming has also been performed block-wise. A significa

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Wang, Meng Hong, Chen Meng Ji, and Shan Shan Luo. "Research Based on Modal Curvature and Wavelet Transform for Identifying Damage of Reticulated Shell Structures." Applied Mechanics and Materials 501-504 (January 2014): 905–10. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.905.

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In this paper, a research is carried on to identify damage of reticulated shell structures based on the combination of modal curvature method and wavelets transform method. Take a scaled model of the reticulated shell structure as an example to analyze, the cross section of one member supposed to have a slight damage of stiffness reduction. In order to locate the damage, modal curvatures of the structure are taken as damage indexes to perform continuous wavelet transform. Results of the numerical analysis indicate that the difference of wavelet transform coefficients of modal curvature can be

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Guillén, Daniel, Gina Idárraga-Ospina, and Camilo Cortes. "A New Adaptive Mother Wavelet for Electromagnetic Transient Analysis." Journal of Electrical Engineering 67, no. 1 (2016): 48–55. http://dx.doi.org/10.1515/jee-2016-0007.

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Abstract Wavelet Transform (WT) is a powerful technique of signal processing, its applications in power systems have been increasing to evaluate power system conditions, such as faults, switching transients, power quality issues, among others. Electromagnetic transients in power systems are due to changes in the network configuration, producing non-periodic signals, which have to be identified to avoid power outages in normal operation or transient conditions. In this paper a methodology to develop a new adaptive mother wavelet for electromagnetic transient analysis is proposed. Classification

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PATIL, G. M., K. SUBBA RAO, U. C. NIRANJAN, and K. SATYANARAYAN. "EVALUATION OF QRS COMPLEX BASED ON DWT COEFFICIENTS ANALYSIS USING DAUBECHIES WAVELETS FOR DETECTION OF MYOCARDIAL ISCHAEMIA." Journal of Mechanics in Medicine and Biology 10, no. 02 (2010): 273–90. http://dx.doi.org/10.1142/s0219519410003356.

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This paper presents a new approach in the field of electrocardiogram (ECG) feature extraction system based on the discrete wavelet transform (DWT) coefficients using Daubechies Wavelets. Real ECG signals recorded in lead II configuration are chosen for processing. The ECG signal was acquired by a battery operated, portable ECG data acquisition and signal processing module. In the second step the ECG signal was denoised using soft thresholding with Symlet4 wavelet. Further denoising was achieved by removing the corresponding wavelet coefficients at higher levels of decomposition. Later the ECG

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Angreni, Puce, and Melda Juliza. "Comparison of Methods ARIMA and MAR Models with MODWT Decomposition on Non-Stationary Data." INSOLOGI: Jurnal Sains dan Teknologi 2, no. 2 (2023): 392–99. http://dx.doi.org/10.55123/insologi.v2i2.1888.

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The forecasting methods used in this study are Autoregressive Integrated Moving Average (ARIMA) and Multiscale Autoregressive (MAR). The ARIMA model does not include predictor variables in the model. The MAR model is a model that performs the transformation process using wavelets. The MAR model adopts an autoregressive time series (AR) model with wavelet coefficients and scale coefficients as predictors. The wavelet coefficient and scale are obtained by decomposition using Maximal Overlap Discrete Wavelet Transformation (MODWT). MODWT functions to describe data based on the level of each wavel

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Cai, Zheng, and Shao Hua Tao. "An Image De-Noising Method Using Directions of Wavelet Decomposition Sub-Bands." Applied Mechanics and Materials 130-134 (October 2011): 3058–61. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.3058.

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In this paper, an image de-noising method using directions of wavelet decomposition sub-bands is proposed. Wavelet coefficients are correlated in a small area, and the wavelet transform uses wavelet coefficients in three directions to describe image information, so in each sub-band the proposed method only calculates neighboring wavelet coefficients in a certain direction rather than in eight directions. Compared with other wavelet de-noising methods, the proposed method can achieve higher peak signal to noise ratio.

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CHEN, YING, ZHI-CHENG JI, and CHUN-JIAN HUA. "EFFICIENT STATISTICAL MODELING OF WAVELET COEFFICIENTS FOR IMAGE DENOISING." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (2009): 629–41. http://dx.doi.org/10.1142/s0219691309003136.

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Statistical modeling of wavelet coefficients is a critical issue in wavelet domain signal processing. By analyzing the defects of other existing methods, and exploiting the local dependency of wavelet coefficients, an efficient statistical model is proposed. Improved variance estimation of the local wavelet coefficients can be obtained using the new model. Then we apply an approximate minimum mean squared error (MMSE) estimation procedure to restore the wavelet image coefficients. The modeling process is computational cost saving, and the denoising experiments show the algorithm outperforms ot

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Kazantsev, S., A. Pavlov, and O. Chekha. "Wavelet transforms of the time series of small wholesale prices in the agricultural sector." IOP Conference Series: Earth and Environmental Science 937, no. 3 (2021): 032075. http://dx.doi.org/10.1088/1755-1315/937/3/032075.

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Abstract The article provides a wavelet analysis of small wholesale prices for white cabbage in Rostov-on-Don from 2017 to 2020 year. Approximation coefficients show a steady trend, the detailing coefficients reflect seasonal and insignificant temporary price fluctuations. The constituent scaling approximation coefficients and the detailing components are highlighted in the form of separate graphs. The series was decomposed up to the 6th level using the Haar and Daubechies wavelets.

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Zhou, Guang-Dong, You-Liang Ding, and Ai-Qun Li. "Evolutionary Spectra Estimation of Field Measurement Typhoon Processes Using Wavelets." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/945203.

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This paper presents a wavelet-based method for estimating evolutionary power spectral density (EPSD) of nonstationary stochastic oscillatory processes and its application to field measured typhoon processes. The EPSD, which is deduced in a closed form based on the definition of the EPSD and the algorithm of the continuous wavelet transform, can be formulated as a sum of squared moduli of the wavelet functions in time domain modulated by frequency-dependent coefficients that relate to the squared values of wavelet coefficients and two wavelet functions with different time shifts. A parametric s

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Fan, Yongkai, Qian Hu, Yun Pan, et al. "A study on optimally constructed compactly supported orthogonal wavelet filters." Computer Science and Information Systems, no. 00 (2021): 52. http://dx.doi.org/10.2298/csis210410052f.

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Compactly supported orthogonal wavelet filters are extensively applied to the analysis and description of abrupt signals in fields such as multimedia. Based on the application of an elementary method for compactly supported orthogonal wavelet filters and the construction of a system of nonlinear equations for filter coefficients, we design compactly supported orthogonal wavelet filters, in which both the scaling and wavelet functions have many vanishing moments, by approximately solving the system of nonlinear equations. However, when solving such a system about filter coefficients of compactl

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Tran, Hai, and Hirotsugu Inoue. "IMPACT FORCE RECONSTRUCTION USING WAVELET DECONVOLUTION TECHNIQUE." ASEAN Engineering Journal 8, no. 1 (2018): 53–66. http://dx.doi.org/10.11113/aej.v8.15498.

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Reconstruction or deconvolution of impact force history from corresponding impact responses such as strain, acceleration, and displacement has been considered as a useful indirect method for measuring the impact force. However, due to the ill-posed nature of deconvolution problem, impact force is often inaccurately and unstably reconstructed. This paper introduces and applies the deconvolution technique using wavelets as a robust method for reconstructing impact force with the advantageous properties of wavelets. First, an analytical process of impact force reconstruction by using the wavelet

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Wang, Tingzhong, Lingli Zhu, Miaomiao Fu, Tingting Zhu, and Ping He. "Repetitive Transient Extraction Using the Optimized SES Entropy Wavelet for Fault Diagnosis of Rotating Machinery." Shock and Vibration 2021 (December 20, 2021): 1–12. http://dx.doi.org/10.1155/2021/8290717.

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Repetitive transients are usually generated in the monitoring data when a fault occurs on the machinery. As a result, many methods such as kurtogram and optimized Morlet wavelet and kurtosis method are proposed to extract the repetitive transients for fault diagnosis. However, one shortcoming of these methods is that they are constructed based on the index of kurtosis and are sensitive to the impulsive noise, leading to failure in accurately diagnosing the fault of the machinery operating under harsh environment. To address this issue, an optimized SES entropy wavelet method is proposed. In th

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Taranenko, Yuri, Ruslan Mygushchenko, Olga Kropachek, Grigoriy Suchkov, and Yuri Plesnetsov. "Minimization of errors in discrete wavelet filtering of signals during ultrasonic measurements and testing." Ukrainian Metrological Journal, no. 4 (December 30, 2021): 57–62. http://dx.doi.org/10.24027/2306-7039.4.2021.250433.

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Error minimizing methods for discrete wavelet filtering of ultrasonic meter signals are considered. For this purpose, special model signals containing various measuring pulses are generated. The psi function of the Daubechies 28 wavelet is used to generate the pulses. Noise is added to the generated pulses. A comparative analysis of the two filtering algorithms is performed. The first algorithm is to limit the amount of detail of the wavelet decomposition coefficients in relation to signal interference. The minimum value of the root mean square error of wavelet decomposition signal deviation w

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Zhu, Zhi Yong. "A Novel Image Fusion Approach Based on Rough Set and Wavelet Analysis." Key Engineering Materials 439-440 (June 2010): 1069–74. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.1069.

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The goal of image fusion is to combine a high-quality image from multi-image about the same object. The paper presents an image fusion scheme based on wavelet transform and rough set. Firstly, the two images are decomposed by orthogonal wavelet; the image’s wavelet coefficients are got. Comparing with the two image’s wavelet coefficients, wavelet coefficients’ matrix is composed of maximum absolute value, the fused image is obtained by the inverse wavelet transform. The last section of the paper verifies the method by experiment and gets the good experimental results.

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Saneva, Katerina. "Asymptotic behaviour of wavelet coefficients." Integral Transforms and Special Functions 20, no. 3-4 (2009): 333–39. http://dx.doi.org/10.1080/10652460802568200.

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Ehrich, Sven. "Explicit inequalities for wavelet coefficients." Applicable Analysis 78, no. 1-2 (2001): 1–8. http://dx.doi.org/10.1080/00036810108840921.

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Abramovich, Felix, and Yoav Benjamini. "Adaptive thresholding of wavelet coefficients." Computational Statistics & Data Analysis 22, no. 4 (1996): 351–61. http://dx.doi.org/10.1016/0167-9473(96)00003-5.

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Alaifari, Rima, Francesca Bartolucci, and Matthias Wellershoff. "Unique wavelet sign retrieval from samples without bandlimiting." Proceedings of the American Mathematical Society, Series B 11, no. 30 (2024): 330–44. http://dx.doi.org/10.1090/bproc/201.

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We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multiwavelet frame coefficients \[ { | W ϕ i f ( α m β n , α m ) | : i ∈ { 1 , 2 , 3 } , m , n ∈ Z } \{\lvert \mathcal {W}_{\phi _i} f(\alpha ^{m}\beta n,\alpha ^{m}) \rvert : i\in \{1,2,3\}, m,n\in \mathbb {Z}\} \] for every α > 1 , β > 0 \alpha >1,\beta >0 with β ln ⁡ ( α ) ≤ 4 π / ( 1 + 4 p ) \beta \ln (\alpha )\leq 4\pi /(1+4p) , p > 0 p>0 , when

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Chen, Bin, Quan Qin, and Xu Gan Zhang. "Image De-Noising in Mixed Noises Based on Wavelet Transform." Advanced Materials Research 562-564 (August 2012): 1861–65. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1861.

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A method of image de-noising in mixed noises based on wavelet transform is presented. Firstly, 2D multi-scale wavelets transforming the images to get the low-frequency sub-band images and the high-frequency sub-band images. Secondly, de-noising both the low-frequency sub-band images with the improved neighborhood average filters and the high-frequency sub-bands images with the improved wavelet threshold method. Lastly, wavelet refactoring the treated sub-band wavelet coefficients to get the de-noised images. The result shows that, this algorithm not only de-noises the image mixed noise, but al

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