Journal articles: 'Wavelet coefficients'

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DEBNATH, LOKENATH, and SARALEES NADARAJAH. "POPULAR WAVELET MODELS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (July 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 (January 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 illustrated.

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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 (March 25, 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 basis of our proposed method is established through the analysis of wavelet threshold theory. To keep the original structure of wavelet coefficients unchanged, we introduce the concept of state quantity of wavelet coefficients and obtain the corresponding state quantity of wavelet coefficients using normalization. The denoising wavelet coefficient is obtained by performing a fourth-order anisotropic diffusion of the state quantities. This paper takes image edge feature extraction as the experimental content and image edges are detected by the module of the wavelet coefficients. The effectiveness of the proposed algorithm is objectively verified from three aspects: denoising effect, edge continuity, and accuracy. The experimental results show that the proposed algorithm can obtain continuous and precise image edges. The algorithm presented in this paper also applies to texture images. Compared with other algorithms, the edges image obtained by this scheme shows advantages in terms of noise removal and edge protection.

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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 coefficients while at the same time preserves the target spectral characters. As a result, the inverse wavelet transform is applied to generate stationary wind velocity history through the given wavelet coefficients. A numerical example to illustrate the application of the proposed method for the simulation of a bridge wind velocity ﬁeld is provided.

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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 hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of theCℓ-functions.

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Jansen, Maarten. "Non-equispaced B-spline wavelets." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 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 fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.

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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 typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.

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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 recover the original coefficients from the noisy wavelet coefficients, and so as to achieve the aim of denoising. Experimental results show that our method is not only better than many of the current denoising methods in the peak signal to noise ratio (PSNR), but also obtained better visual effect.

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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 polynomials and compression of spline-wavelet decomposition are presented.

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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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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 (July 6, 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 through applying wavelet transform. To enhance damage identification, first, the edges’ effect of wavelet transform was removed, then a higher accuracy was observed by summing the wavelet coefficients in all scale factors for each mode shape and the wavelet coefficients for all mode shapes. The article also presents a quantitative measure to compare different wavelets.

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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 DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

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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 (December 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 (June 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 coefficients. In the second step, ECG signal is decomposed to three levels using the optimum wavelet and reconstructed. From the reconstructed signal, the range of error signal is calculated and it is compared with the performance of other suitable wavelets already available in the literature. The optimum wavelet gives the maximum error range as 10-14–10-11 which is better than that of other wavelets existing in the literature. In the third step, the baseline wandering is removed from the ECG signal for better detection of QRS complex. The optimum wavelet detects all R peaks of all records. That is using optimum wavelet 100% sensitivity and positive predictions are achieved. Based on the performance, it is confirmed that optimum wavelet is more suitable for ECG signal.

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Mathew, K., and S. Shibu. "Reconstruction of Wavelet Coefficients." International Journal of Computer Applications 97, no. 15 (July 18, 2014): 27–34. http://dx.doi.org/10.5120/17086-7542.

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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 (September 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 utilized. Training data are used to construct probability distributions required for the computation of the entropy and mutual information. In our data analysis, we have used machine data acquired from a single cylinder engine under a series of induced faults in a test environment. The objective of the experiment was to evaluate the performance of the informative wavelet algorithm for the accuracy of classification results using a real-world machine data and to examine to what extent the results were influenced by different analyzing wavelets chosen for data analysis. Accuracy of classification results as related to the correlation structure of the coefficients is also discussed in the paper.

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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 filters was constructed, and the optimum sampling time of the wavelet filtering of the investigated signal was calculated for determination of the propagation and rotational breakdown in the GTE turbocompressor. According to this scheme, among the wavelets of Dobeski, Simlet, Koefleta, and Meyer's discrete wavelet, for studying the air pressure signal at the compressor during bursting processes, the first were selected by the Dobeches and Symmetes wavelets of the 2nd order according to their filtration rate. Considering high speed and characteristics of the description of the occurrence of excite phenomena by means of a fast Fourier transform to the distribution of the wavelet coefficients of the air pressure signal by turbocompressor, for the diagnosis of unstable flows occurring in the gas path of the gas turbine trajectory (surging and rotary breakdown), the Dobeski wavelet was selected 2nd order. At the same time, to monitor the wavelet coefficients behavior, the detail of the investigated signal is necessary at the 7th level of decomposition. Thus, the obtained results allow to carry out further analysis of breakdown processes using low-order wavelets.

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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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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 (March 1, 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 statistical hypothesis test is employed to select the informative EWT coefficients. Only the selected coefficients are used for Microarray Data Classification (MDC) by the Support Vector Machine (SVM). Computational experiments are employed on five microarray datasets; colon, breast, leukemia, CNS and ovarian to test the developed cancer classification system. The obtained results demonstrate that EWT coefficients with SVM emerged as an effective approach with no misclassification for MDC system.

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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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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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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 analytically defined by some kind of a finite hypergeometric series (connection coefficients).

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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 (November 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 approximating and detailing components. Continuous and discrete wavelet transforms are widely used [2] for signal analysis in modern communication channels. The set of functions defining the wavelet transform belongs to the space of square-integrable functions on a straight line and provides a necessary condition for constructing constructions of nonlinear codes based on the theory of wavelet decomposition. As is known, in the process of wavelet analysis, the signal is decomposed along the orthogonal basis formed by shifts of the wavelet function. A distinctive feature of this approach is that convolution of the signal with wavelets allows us to identify the characteristic features of the signal in the area of localization of these wavelets. To perform computational calculations, you need a set of scaling function coefficients and a wavelet. The wavelet transform matrix depends on the coefficients of the scaling function. The results presented in the article describe a new approach to ensuring data integrity in communication channels using nvcs. A computational example is presented.

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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 two wavelet advantages. (2) The primary period value identified using Mexh eco-used wavelet than using its original wavelet is closer to the true one, while Morl eco-used wavelet helps find all changes in the period earlier. (3) For the same wavelet function, with its period enlarging, its primary period can be found in a smaller scale, inversely found later.

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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 (February 2, 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 conversion time. In addition, the zoom factor can be less than two. The Mallat algorithm uses non-symmetric wavelets, and to increase the accuracy of the reconstruction, large-order wavelets are obtained, which increases the transformation time. On the contrary, in our algorithm, depending on the sample length, the wavelets are symmetric and the time of the inverse wavelet transform can be faster by 6–7 orders of magnitude compared to the direct numerical calculation of the convolution. At the same time, the quality of analysis and the accuracy of signal reconstruction increase because the wavelet transform is strictly orthogonal.

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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 (July 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 is also studied. Finally, a scheme based on the admissible wavelet packet has also been proposed and the results are discussed and compared with the frequently used Mel Frequency Cepstral Coefficients based features. The recognition performance of these features is further evaluated in the presence of different level of additive white Gaussian noise.

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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. This localization can be applied to any arbitrary region of the beam by choosing optimum reduction matrix and obtaining exact solutions with an acceptable reduced size of the problem.

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REVATHY, K., G. RAJU, and S. R. PRABHAKARAN NAYAR. "IMAGE ZOOMING BY WAVELETS." Fractals 08, no. 03 (September 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 significant drawback of the method is that the scaling factor should be power of 2.

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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 used to locate damage roughly, while the wavelet transform coefficients of modal curvature difference can be used to locate damage more precisely with easier and more reliable data processing. So it is clear that the damage identification based on modal curvature and wavelet transform is quite effective.

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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 (January 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 is carried out with an innovative technique based on adaptive wavelets, where filter bank coefficients will be adapted until a discriminant criterion is optimized. Then, its corresponding filter coefficients will be used to get the new mother wavelet, named wavelet ET, which allowed to identify and to distinguish the high frequency information produced by different electromagnetic transients.

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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 should be embedded into next wavelet coefficient. If the sum of wavelet coefficients is large, the wavelet coefficients of next level should be embedded by secret information. Finally, the stego-image can be obtained by using the inverse wavelet transform. From the experimental results, the proposed method could effectively keep the identity of histogram for wavelet coefficients and maintain a good visual quality of stego-image.

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Saneva, Katerina. "Asymptotic behaviour of wavelet coefficients." Integral Transforms and Special Functions 20, no. 3-4 (April 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 (June 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 (August 1996): 351–61. http://dx.doi.org/10.1016/0167-9473(96)00003-5.

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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 (June 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 data files were converted to .txt files and subsequently to. mat files before being imported into the Matlab 7.4.0 environment for the computation of the decomposition coefficients. The QRS complexes were grouped as normal or myocardial ischaemic ones based on these decomposition coefficients. The algorithm developed by us was evaluated with control database comprising 120 records and validated using 60 records making up test database. By using the DWT coefficients, we have successfully achieved the myocardial ischaemia detection rates up to 97.5% with the technique developed by us for control data and up to 100% for validation test data.

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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 (December 1, 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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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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Fan, Yongkai, Qian Hu, Yun Pan, Chaosheng Huang, Chao Chen, Kuan-Ching Li, Weiguo Lin, Xingang Wu, LI Yaxuan, and Wenqian Shang. "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 compactly supported wavelets, the most widely used method, the Newton Iteration method, cannot converge to the solution if the selected initial value is not near the exact solution. For such, we propose optimization algorithms for the Gauss-Newton type method that expand the selection range of initial values. The proposed method is optimal and promising when compared to other works, by analyzing the experimental results obtained in terms of accuracy, iteration times, solution speed, and complexity.

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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 (September 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 other approaches in peak-signal-to-noise ratio (PSNR).

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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 study is conducted to examine the efficacy of the wavelet-based estimation method and the accuracy of different wavelets. The results indicate that all of the estimated EPSDs have acceptable accuracy in engineering application and the Morlet transform can provide desirable estimations in both time and frequency domains. Finally, the proposed method is adopted to investigate the time-frequency characteristics of the Typhoon Matsa measured in bridge site. The nonstationary energy distribution and stationary frequency component during the whole process are found. The work in this paper may promote an improved understanding of the nonstationary features of typhoon winds.

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Tran, Hai, and Hirotsugu Inoue. "IMPACT FORCE RECONSTRUCTION USING WAVELET DECONVOLUTION TECHNIQUE." ASEAN Engineering Journal 8, no. 1 (June 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 technique in terms of scaling and translating the Haar wavelet is formulated. The unknown impact force is represented by the expanded coefficients at different scales and shifts of Haar wavelet which is compactly supported in the time domain (finite in time). Then, based on the governing equation of impact force deconvolution, the reconstruction process of these expanded coefficients is formulated. Second, a structural model is built by finite element method to obtain impulse response function numerically. After that, the wavelet technique is applied to reconstruct the impact forces acting on the structure to verify its effectiveness. The comparisons between reconstructed forces and finite element analysis results demonstrate the success of the present technique in accurately reconstructing the numerical impact forces acting on the thin-walled column. These achievements show remarkable ability of the wavelet technique for reconstructing accurately any input forces.

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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 the proposed method, the optimized parameters including bandwidth and central frequency of Morlet wavelets are selected. Then, based on the wavelet coefficients decomposed using the optimized Morlet wavelet, the SES entropy is calculated to select the scales of wavelet coefficients. Finally, the repetitive transients are reconstructed based on the denoising wavelet coefficients of the selected scales. One simulation case and vibration data collected from the experimental setup are used to verify the effectiveness of the proposed method. The simulated and experimental analyses showed that the signal-to-noise ratio (SNR) of the proposed method has the largest value. Specifically, the SNR in the experimental analysis of the proposed method is 0.6, while that of the other three methods is 0.043, 0.0065, and 0.0045, respectively. Therefore, the result shows that the proposed method is superior to the traditional methods for repetitive transient extraction from the vibration data suffered from impulsive noise.

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Sheikh, N. A., and M. Mursaleen. "Infinite matrices, wavelet coefficients and frames." International Journal of Mathematics and Mathematical Sciences 2004, no. 67 (2004): 3695–702. http://dx.doi.org/10.1155/s0161171204312457.

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We study the action ofAonf∈L2(ℝ)and on its wavelet coefficients, whereA=(almjk)lmjkis a double infinite matrix. We find the frame condition forA-transform off∈L2(ℝ)whose wavelet series expansion is known.

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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 which is restored at each level from the initial signal without noise is determined. The second algorithm uses a separate threshold for each level of wavelet decomposition to limit the magnitude of the detail coefficients that are proportional to the standard deviation. Like in the first algorithm, the task is to determine the level of wavelet decomposition at which the minimum standard error is achieved. A feature of both algorithms is an expanded base of discrete wavelets ‒ families of Biorthogonal, Coiflet, Daubechies, Discrete Meyer, Haar, Reverse Biorthogonal, Symlets (106 in total) and threshold functions garotte, garrote, greater, hard, less, soft (6 in total). The model function uses random variables in both algorithms, so the averaging base is used to obtain stable results. Given features of algorithm construction allowed to reveal efficiency of ultrasonic signal filtering on the first algorithm presented in the form of oscilloscopic images. The use of a separate threshold for limiting the number of detail coefficients for each level of discrete wavelet decomposition using the given wavelet base and threshold functions has reduced the filtering error.

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Irfan, Nagma, and A. H. Siddiqi. "A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics." International Journal of Engineering Mathematics 2015 (August 31, 2015): 1–9. http://dx.doi.org/10.1155/2015/789675.

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The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ν, ν>-1, using wavelets. The philosophy behind the proposed algorithm is to replace the part tf(t) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing Fν(p) as a Fourier-Bessel series with coefficients depending strongly on the input function tf(t). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

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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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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 also preserves the image edges and details well.

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Yang, Zhibo, Xuefeng Chen, Yumin He, Zhengjia He, and Jie Zhang. "The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method." Shock and Vibration 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/738162.

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A B-spline wavelet on interval (BSWI) finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch) are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.

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Makhov, V. E., V. V. Shirobokov, A. V. Emelyanov, and A. I. Potapov. "INVESTIGATION OF ALGORITHMS OF DETECTING OF THE CHARACTERISTICS OF REMOTE OBJECTS IN OPTOELECTRONIC SYSTEMS BY THE METHOD OF WAVELET TRANSFORMATION." Kontrol'. Diagnostika, no. 286 (April 2022): 20–31. http://dx.doi.org/10.14489/td.2022.04.pp.020-031.

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The issues of the accuracy of measuring the coordinates and size of objects observed by an optical system by the methods of single and double continuous wavelet transform in their image are considered. It is shown that the use of the second continuous wavelet transform to the curves of the coefficients of the first transform leads to an increase in the extrema of the scalegram and the smoothness of the curves of the coefficients, providing more than two times higher coordinate sensitivity of determining the position and orientation of objects. The use of different types of wavelets in each continuous wavelet transform of signals gives many options for the curves of the coefficients of the continuous wavelet transform and can be used for additional filtering of noise, taking into account the nature of objects. The parallel use of mathematical models and real objects in a neural network for determining the coordinates of signals and their characteristics is proposed, which leads to an increase in accuracy for each type of object, the possibility of constructing intelligent control devices for outer space. Using the example of an experimental installation of two synchronously movable optoelectronic systems, the accuracy of combining images of objects in multiplexing systems from different digital sources is demonstrated.

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Journal articles on the topic 'Wavelet coefficients'

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