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Journal articles on the topic 'Continuous wavelet analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

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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Stark, Hans-Georg. "Continuous wavelet transform and continuous multiscale analysis." Journal of Mathematical Analysis and Applications 169, no. 1 (September 1992): 179–96. http://dx.doi.org/10.1016/0022-247x(92)90110-y.

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Wachowiak, Mark P., Renata Wachowiak-Smolíková, Michel J. Johnson, Dean C. Hay, Kevin E. Power, and F. Michael Williams-Bell. "Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170250. http://dx.doi.org/10.1098/rsta.2017.0250.

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Theoretical and practical advances in time–frequency analysis, in general, and the continuous wavelet transform (CWT), in particular, have increased over the last two decades. Although the Morlet wavelet has been the default choice for wavelet analysis, a new family of analytic wavelets, known as generalized Morse wavelets, which subsume several other analytic wavelet families, have been increasingly employed due to their time and frequency localization benefits and their utility in isolating and extracting quantifiable features in the time–frequency domain. The current paper describes two practical applications of analysing the features obtained from the generalized Morse CWT: (i) electromyography, for isolating important features in muscle bursts during skating, and (ii) electrocardiography, for assessing heart rate variability, which is represented as the ridge of the main transform frequency band. These features are subsequently quantified to facilitate exploration of the underlying physiological processes from which the signals were generated. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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Gulai, A. V., and V. M. Zaitsev. "INTELLIGENT TECHNOLOGY OF WAVELET ANALYSIS OF VIBRATION SIGNALS." Doklady BGUIR, no. 7-8 (December 29, 2019): 101–8. http://dx.doi.org/10.35596/1729-7648-2019-126-8-101-108.

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During solution of engineering problems of machinery dynamics a need of revealing the harmonic components often arises in the narrow timing gate. This requires the use of wavelet-transformation oscillation methods and introduction of intelligent systems to hardware and software used in the experiment. The wavelet is considered as a short in time signal functional window, which has its internal structure in the form of a fading wavelike burst, and it is characterized by a scale of display of certain events in the field of the signal frequency spectrum, as well as and by time axis shifts. Complex-functioned continuous functions of real arguments (Daubechies wavelets, Gaussian wavelets, MHat-wavelets), complex-valued functions of real arguments (Morlet and Paul wavelets), as well as real discrete functions (HААRT- and FHat-wavelets) are used as wavelet functions. The wavelet analysis method of vibration signals is disclosed at acoustic diagnostics of machines and mechanisms. Digital implementation of discrete indications of wavelets with the subsequent visualization of results in the form of scalotons is the mathematical basis of the algorithm for procession of vibration signals. It has been suggested that engineering analysis and reconstruction of signals should be implemented by means of directed and reverse continuous wavelet conversions, which are discrete by arguments. The structural and functional scheme of the multichannel system of the intelligent wavelet analysis of vibration signals in machines has been considered. The intelligent system for study of vibration signals makes it possible to form the totality of photographic parameters, when scalotons are calculated by wavelet functions. An example of experimental implementation of the wavelet conversion method of vibration signals parameters is shown. Results of scalotons calculation are shown, when MHat-wavelet and DOG-wavelet are used.

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Qin, Jun, and Pengfei Sun. "Applications and Comparison of Continuous Wavelet Transforms on Analysis of A-wave Impulse Noise." Archives of Acoustics 40, no. 4 (December 1, 2015): 503–12. http://dx.doi.org/10.1515/aoa-2015-0050.

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Abstract Noise induced hearing loss (NIHL) is a serious occupational related health problem worldwide. The A-wave impulse noise could cause severe hearing loss, and characteristics of such kind of impulse noise in the joint time-frequency (T-F) domain are critical for evaluation of auditory hazard level. This study focuses on the analysis of A-wave impulse noise in the T-F domain using continual wavelet transforms. Three different wavelets, referring to Morlet, Mexican hat, and Meyer wavelets, were investigated and compared based on theoretical analysis and applications to experimental generated A-wave impulse noise signals. The underlying theory of continuous wavelet transform was given and the temporal and spectral resolutions were theoretically analyzed. The main results showed that the Mexican hat wavelet demonstrated significant advantages over the Morlet and Meyer wavelets for the characterization and analysis of the A-wave impulse noise. The results of this study provide useful information for applying wavelet transform on signal processing of the A-wave impulse noise.

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6

Alhasan, Ahmad, David J. White, and Kris De Brabanterb. "Continuous wavelet analysis of pavement profiles." Automation in Construction 63 (March 2016): 134–43. http://dx.doi.org/10.1016/j.autcon.2015.12.013.

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7

Lee, Sang Kwon, and Jang Sun Sim. "Development of Spike Wavelet Analysis and Its Application to Damage Analysis on Gearbox." Key Engineering Materials 321-323 (October 2006): 1233–36. http://dx.doi.org/10.4028/www.scientific.net/kem.321-323.1233.

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Impulsive sound and vibration signals in gear system are often associated with their faults. Thus these impulsive sound and vibration signals can be used as indicators in condition monitoring of gear system. The traditional continuous wavelet transform has been used for detection of impulsive signals. However, it is often difficult for the continuous wavelet transform to identify spikes at high frequency and meshing frequencies at low frequency simultaneously since the continuous wavelet transform is to apply the linear scaling (a-dilation) to the mother wavelet. In this paper, the spike wavelet transform is developed to extract these impulsive sound and vibration signals. Since the spike wavelet transform is to apply the non-linear scaling, it has better time resolution at high frequency and frequency resolution at low frequency than that of the continuous wavelet transform respectively. The spike wavelet transform can be, therefore, used to detect fault position clearly without the loss of information for the damage of a gear system. The spike wavelet transform is successfully is applied to detection of the gear fault with tip breakage.

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8

Lin, En-Bing, and Paul C. Liu. "A discrete wavelet analysis of freak waves in the ocean." Journal of Applied Mathematics 2004, no. 5 (2004): 379–94. http://dx.doi.org/10.1155/s1110757x0430611x.

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A freak wave is a wave of very considerable height, ahead of which there is a deep trough. A case study examines some basic properties developed by performing wavelet analysis on a freak wave. We demonstrate several applications of wavelets and discrete and continuous wavelet transforms on the study of a freak wave. A modeling setting for freak waves will also be mentioned.

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9

STASZEWSKI, W. J., and K. WORDEN. "WAVELET ANALYSIS OF TIME-SERIES: COHERENT STRUCTURES, CHAOS AND NOISE." International Journal of Bifurcation and Chaos 09, no. 03 (March 1999): 455–71. http://dx.doi.org/10.1142/s0218127499000304.

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The continuous and orthogonal wavelet transforms are used to analyze time-series data. The analysis involves signal decomposition into scale components using both Grossman–Morlet and Daubechies type wavelets. A number of simulated and experimental data vectors exhibiting different types of coherent structures, chaos and noise is analyzed. The study shows that wavelet analysis provides a unifying framework for the description of many phenomena in time-series.

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Ji, Ning, Hui Zhou, Kaifeng Guo, Oluwarotimi Samuel, Zhen Huang, Lisheng Xu, and Guanglin Li. "Appropriate Mother Wavelets for Continuous Gait Event Detection Based on Time-Frequency Analysis for Hemiplegic and Healthy Individuals." Sensors 19, no. 16 (August 8, 2019): 3462. http://dx.doi.org/10.3390/s19163462.

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Gait event detection is a crucial step towards the effective assessment and rehabilitation of motor dysfunctions. Recently, the continuous wavelet transform (CWT) based methods have been increasingly proposed for gait event detection due to their robustness. However, few investigations on determining the appropriate mother wavelet with proper selection criteria have been performed, especially for hemiplegic patients. In this study, the performances of commonly used mother wavelets in detecting gait events were systematically investigated. The acceleration signals from the tibialis anterior muscle of both healthy and hemiplegic subjects were recorded during ground walking and the two core gait events of heel strike (HS) and toe off (TO) were detected from the signal recordings by a CWT algorithm with different mother wavelets. Our results showed that the overall performance of the CWT algorithm in detecting the two gait events was significantly different when using various mother wavelets. By using different wavelet selection criteria, we also found that the accuracy criteria based on time-error minimization and F1-score maximization could provide the appropriate mother wavelet for gait event detection. The findings from this study will provide an insight on the selection of an appropriate mother wavelet for gait event detection and facilitate the development of adequate rehabilitation aids.

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BENSON, NOAH C., and VALERIE DAGGETT. "WAVELET ANALYSIS OF PROTEIN MOTION." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 04 (July 2012): 1250040. http://dx.doi.org/10.1142/s0219691312500403.

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As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase.

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12

Duval-Destin, M., M. A. Muschietti, and B. Torresani. "Continuous Wavelet Decompositions, Multiresolution, and Contrast Analysis." SIAM Journal on Mathematical Analysis 24, no. 3 (May 1993): 739–55. http://dx.doi.org/10.1137/0524045.

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13

Liu, Bei, and Wenchang Sun. "Homogeneous approximation property for continuous wavelet transforms." Journal of Approximation Theory 155, no. 2 (December 2008): 111–24. http://dx.doi.org/10.1016/j.jat.2008.03.010.

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14

Prasad, Akhilesh, Ashutosh Mahato, Vishal Singh, and Madan Dixit. "The continuous fractional Bessel wavelet transformation." Boundary Value Problems 2013, no. 1 (2013): 40. http://dx.doi.org/10.1186/1687-2770-2013-40.

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15

Gautam, Apoorv. "ECG Analysis using Continuous Wavelet Transform (CWT)." IOSR Journal of Engineering 02, no. 04 (April 2012): 632–35. http://dx.doi.org/10.9790/3021-0204632635.

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16

Radha, R., and K. Sarvesh. "Hardy’s theorem for the continuous wavelet transform." Journal of Pseudo-Differential Operators and Applications 11, no. 2 (November 25, 2019): 869–77. http://dx.doi.org/10.1007/s11868-019-00318-x.

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17

Dziedziech, Kajetan, Alexander Nowak, Alexander Hasse, Tadeusz Uhl, and Wiesław J. Staszewski. "Wavelet-based analysis of time-variant adaptive structures." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170245. http://dx.doi.org/10.1098/rsta.2017.0245.

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Wavelet analysis is applied to identify the time-variant dynamics of adaptive structures. The wavelet-based power spectrum of the structural response, wavelet-based frequency response function (FRF) and wavelet-based coherence are used to identify continuously and abruptly varying natural frequencies. A cantilever plate with surface-bonded macro fibre composite—which alters the structural stiffness—is used to demonstrate the application of the methods. The results show that the wavelet-based input–output characteristics—i.e. the FRF and coherence—can identify correctly the dynamics of the analysed time-variant system and reveal the varying natural frequency. The wavelet-based coherence can be used not only for the assessment of the quality of the wavelet-based FRF but also for the identification. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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18

Zhang, Jin, ShuJun Li, and FanJun Meng. "A method for detecting and locating the gross error of tidal based on wavelet analysis." E3S Web of Conferences 131 (2019): 01036. http://dx.doi.org/10.1051/e3sconf/201913101036.

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Tidal harmonic constants are necessary data for the evaluation of tidal model, tidal prediction and chart datum. Compared with the wavelet multi-scale analysis model, a new method is put forward to detect and locate tidal discrete and continuous gross error. Based on the properties of the wavelets, the wavelet suitable for detecting the gross error of tidal is selected. And taking db6 wavelet as an example, the feasibility and effectiveness of this method are proved by experiments. The results show that the method can not only simultaneously detect and locate discrete gross error and continuous gross based on high frequency information, and can detect and locate the systematic deviation caused by the zero drift according to the low frequency information. Experimental result shows that the method is more simple, the efficiency and accuracy of detecting and locating gross error are improved.

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19

CHRISTENSEN, OLE, BRIGITTE FORSTER, and PETER MASSOPUST. "DIRECTIONAL TIME–FREQUENCY ANALYSIS VIA CONTINUOUS FRAMES." Bulletin of the Australian Mathematical Society 92, no. 2 (April 30, 2015): 268–81. http://dx.doi.org/10.1017/s0004972715000337.

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Grafakos and Sansing [‘Gabor frames and directional time–frequency analysis’, Appl. Comput. Harmon. Anal.25 (2008), 47–67] have shown how to obtain directionally sensitive time–frequency decompositions in $L^{2}(\mathbb{R}^{n})$ based on Gabor systems in $L^{2}(\mathbb{R})$. The key tool is the ‘ridge idea’, which lifts a function of one variable to a function of several variables. We generalise their result in two steps: first by showing that similar results hold starting with general frames for $L^{2}(\mathbb{R}),$ in the settings of both discrete frames and continuous frames, and second by extending the representations to Sobolev spaces. The first step allows us to apply the theory to several other classes of frames, for example wavelet frames and shift-invariant systems, and the second one significantly extends the class of examples and applications. We consider applications to the Meyer wavelet and complex B-splines. In the special case of wavelet systems we show how to discretise the representations using ${\it\epsilon}$-nets.

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20

Brandner, Paul A., James A. Venning, and Bryce W. Pearce. "Wavelet analysis techniques in cavitating flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170242. http://dx.doi.org/10.1098/rsta.2017.0242.

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Cavitating and bubbly flows involve a host of physical phenomena and processes ranging from nucleation, surface and interfacial effects, mass transfer via diffusion and phase change to macroscopic flow physics involving bubble dynamics, turbulent flow interactions and two-phase compressible effects. The complex physics that result from these phenomena and their interactions make for flows that are difficult to investigate and analyse. From an experimental perspective, evolving sensing technology and data processing provide opportunities for gaining new insight and understanding of these complex flows, and the continuous wavelet transform (CWT) is a powerful tool to aid in their elucidation. Five case studies are presented involving many of these phenomena in which the CWT was key to data analysis and interpretation. A diverse set of experiments are presented involving a range of physical and temporal scales and experimental techniques. Bubble turbulent break-up is investigated using hydroacoustics, bubble dynamics and high-speed imaging; microbubbles are sized using light scattering and ultrasonic sensing, and large-scale coherent shedding driven by various mechanisms are analysed using simultaneous high-speed imaging and physical measurement techniques. The experimental set-up, aspect of cavitation being addressed, how the wavelets were applied, their advantages over other techniques and key findings are presented for each case study. This paper is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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21

Cerejeiras, P., M. Ferreira, U. Kähler, and F. Sommen. "Continuous wavelet transform and wavelet frames on the sphere using Clifford analysis." Communications on Pure & Applied Analysis 6, no. 3 (2007): 619–41. http://dx.doi.org/10.3934/cpaa.2007.6.619.

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22

Baccar, C. "Uncertainty principles for the continuous Hankel Wavelet transform." Integral Transforms and Special Functions 27, no. 6 (February 22, 2016): 413–29. http://dx.doi.org/10.1080/10652469.2016.1148031.

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23

Butaev, Almaz, and Ravshan Ashurov. "On some class of nonseparable continuous wavelet transforms." Applicable Analysis 91, no. 12 (December 2012): 2257–65. http://dx.doi.org/10.1080/00036811.2011.601296.

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24

Rubin, B. "Inversion ofk-Plane Transforms via Continuous Wavelet Transforms." Journal of Mathematical Analysis and Applications 220, no. 1 (April 1998): 187–203. http://dx.doi.org/10.1006/jmaa.1997.5852.

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25

Andreas, Rieder. "The high frequency behaviour of continuous wavelet transforms." Applicable Analysis 52, no. 1-4 (February 1994): 125–41. http://dx.doi.org/10.1080/00036819408840229.

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26

Lang, W. Christopher, and Kyle Forinash. "Time-frequency analysis with the continuous wavelet transform." American Journal of Physics 66, no. 9 (September 1998): 794–97. http://dx.doi.org/10.1119/1.18959.

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27

Dursun, Ali, Serhat Özder, and F. Necati Ecevit. "Continuous wavelet transform analysis of projected fringe patterns." Measurement Science and Technology 15, no. 9 (July 24, 2004): 1768–72. http://dx.doi.org/10.1088/0957-0233/15/9/013.

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28

Kirby, Jon. "Anisotropic Isostatic Analysis Using the Continuous Wavelet Transform." ASEG Extended Abstracts 2003, no. 2 (August 2003): 1. http://dx.doi.org/10.1071/aseg2003ab088.

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29

Antoine, J. P., P. Carrette, R. Murenzi, and B. Piette. "Image analysis with two-dimensional continuous wavelet transform." Signal Processing 31, no. 3 (April 1993): 241–72. http://dx.doi.org/10.1016/0165-1684(93)90085-o.

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30

Tenreiro Machado, J., Fernando B. Duarte, and Gonçalo Monteiro Duarte. "Analysis of Stock Market Indices with Multidimensional Scaling and Wavelets." Mathematical Problems in Engineering 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/819503.

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Stock market indices (SMIs) are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling (MDS). Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

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Indrusiak, M. L. S., A. J. Kozakevicius, and S. V. Möller. "WAVELET ANALYSIS CONSIDERATIONS FOR EXPERIMENTAL NONSTATIONARY FLOW PHENOMENA." Revista de Engenharia Térmica 15, no. 1 (June 30, 2016): 67. http://dx.doi.org/10.5380/reterm.v15i1.62149.

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In this work, wavelet transforms are the analysis tools for studying transient and discontinuous phenomena associated to turbulent flows. The application in quest results from velocity measurements with hot wire anemometry in the transient wake considering a circular cylinder in an aerodynamic channel. Continuous and discrete wavelet transforms are applied and compared with the corresponding results given by the Fourier transform. For the continuous wavelet transform, the Morlet function was adopted as transform basis, and for the discrete case, the Daubechies orthonormal wavelet with 20 null moments. Results using the discrete wavelet packet transform are also presented and compared. A wake past a cylinder was analytically simulated and compared with the actual one, both in transient flow. The ability of the wavelet transforms in the analysis of unsteady phenomena and the potential of the wavelet approach as a complementary tool to the Fourier spectrum for the analysis of stationary phenomena is presented and discussed.

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32

Ma, Huiqin, Wenjiang Huang, Yuanshu Jing, Stefano Pignatti, Giovanni Laneve, Yingying Dong, Huichun Ye, Linyi Liu, Anting Guo, and Jing Jiang. "Identification of Fusarium Head Blight in Winter Wheat Ears Using Continuous Wavelet Analysis." Sensors 20, no. 1 (December 19, 2019): 20. http://dx.doi.org/10.3390/s20010020.

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Fusarium head blight in winter wheat ears produces the highly toxic mycotoxin deoxynivalenol (DON), which is a serious problem affecting human and animal health. Disease identification directly on ears is important for selective harvesting. This study aimed to investigate the spectroscopic identification of Fusarium head blight by applying continuous wavelet analysis (CWA) to the reflectance spectra (350 to 2500 nm) of wheat ears. First, continuous wavelet transform was used on each of the reflectance spectra and a wavelet power scalogram as a function of wavelength location and the scale of decomposition was generated. The coefficient of determination R2 between wavelet powers and the disease infestation ratio were calculated by using linear regression. The intersections of the top 5% regions ranking in descending order based on the R2 values and the statistically significant (p-value of t-test < 0.001) wavelet regions were retained as the sensitive wavelet feature regions. The wavelet powers with the highest R2 values of each sensitive region were retained as the initial wavelet features. A threshold was set for selecting the optimal wavelet features based on the coefficient of correlation R obtained via the correlation analysis among the initial wavelet features. The results identified six wavelet features which include (471 nm, scale 4), (696 nm, scale 1), (841 nm, scale 4), (963 nm, scale 3), (1069 nm, scale 3), and (2272 nm, scale 4). A model for identifying Fusarium head blight based on the six wavelet features was then established using Fisher linear discriminant analysis. The model performed well, providing an overall accuracy of 88.7% and a kappa coefficient of 0.775, suggesting that the spectral features obtained using CWA can potentially reflect the infestation of Fusarium head blight in winter wheat ears.

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Lweesy, K., N. Khasawneh, M. Fraiwan, H. Wenz, H. Dickhaus, and L. Fraiwan. "Classification of Sleep Stages Using Multi-wavelet Time Frequency Entropy and LDA." Methods of Information in Medicine 49, no. 03 (2010): 230–37. http://dx.doi.org/10.3414/me09-01-0054.

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Summary Background: The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomno-graphic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. Objectives: This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. Methods: The use of different mother wave-lets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Results: Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. Conclusions: This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

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Sun, Zuo Yu, Hui Wang, Yong Shan Zhang, and Le Wei Yan. "Random Vibration Analysis for a Building under Evolutionary Random Excitations." Applied Mechanics and Materials 376 (August 2013): 262–66. http://dx.doi.org/10.4028/www.scientific.net/amm.376.262.

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For a building under evolutionary random excitations, a new random vibration analysis based on equivalent excitation method is presented, in which, the equivalent excitation is constructed by using continuous wavelet transform. When the input power spectral density of a seismic excitation is modulated by a time varying function, the continuous wavelet coefficients are calculated firstly by using scales and the evolutionary power spectral density, then the equivalent excitation is constructed by inverse continuous wavelet transform, finally the random vibration analysis is carried out following the procedures of the equivalent excitation method. An example is given to show the whole procedure, in which the special ability of the method for dealing with the evolutionary random excitation is discussed in detail.

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Zhu, Bin, and Wei Dong Jin. "Feature Analysis of Advanced Radar Emitter Signals Based on Continuous Wavelet Transform." Applied Mechanics and Materials 246-247 (December 2012): 1125–29. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.1125.

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For further study the recognition problem of radar emitter signals (RES), the theory of continuous wavelet transform (CWT) and gray moment are introduced into the feature extraction of RES. A new approach for RES feature extraction was proposed based on CWT and gray moment. By using the time-frequency domain characteristics of wavelet analysis and the moment-based method, the CWT coefficients of RES and the changing rules of RES gray moment were researched. The experiment results shows that the wavelet gray moments of the RES take on a rising trend along with the increase of the order, and the four-order wavelet gray moment vector can express the local information of RES more exactly. This is useful for further research on RES feature extracting.

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Guido, Rodrigo Capobianco, Fernando Pedroso, André Furlan, Rodrigo Colnago Contreras, Luiz Gustavo Caobianco, and Jogi Suda Neto. "CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 06 (August 28, 2020): 2030001. http://dx.doi.org/10.1142/s0219691320300017.

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Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

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Luo, G. Y., D. Osypiw, and M. Irle. "On-Line Vibration Analysis with Fast Continuous Wavelet Algorithm for Condition Monitoring of Bearing." Journal of Vibration and Control 9, no. 8 (August 2003): 931–47. http://dx.doi.org/10.1177/10775463030098002.

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The newly developed technique of wavelet transform enables us to observe the evolution in time of the frequency content of a signal. This property makes it very suitable for the detection of vibration transients. However, current algorithms for vibration analysis either have low resolution of features for detailed analysis in the frequency-band scale or are very time consuming. In this paper, we present fast wavelet-based algorithms for vibration analyses. The approximated Morlet wavelet is used to develop an infinite impulse response causal filter with the error kept at an acceptable level. Using this filter, the continuous wavelet transform (CWT) can be computed. The rapid computation of the CWT, together with autocorrelation enhancement, is developed for the detailed on-line vibration analysis. Thus, the raw vibration signal can be continuously processed and monitored, with warning or alarm signals being generated when pre-programmed levels are exceeded. Examples are used to illustrate the application of arbitrary fine frequency-band scale analysis and single specified central frequency in the time domain using the wavelet power spectrum, which enables small defect detection of bearings. Real-time condition monitoring, fault detection, tool wear monitoring, etc., which are related to vibration, can be achieved and implemented with the detailed analysis of vibration signals.

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Verner, Robert, and Gabriel Herbrik. "Bond yields and stock returns comparison using wavelet semblance analysis." Investment Management and Financial Innovations 14, no. 2 (July 27, 2017): 281–89. http://dx.doi.org/10.21511/imfi.14(2-1).2017.12.

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Various measures of resemblance are increasingly applied in confrontation of data samples obtained by different sources. Semblance analysis aims at comparison of two sets of data based on their phase and frequency. Conventional semblance analysis following the Fourier transform has several deficiencies resulting from the transform. To overcome these obstacles, another type of semblance analysis was developed applying the wavelet transform. This paper focuses on semblance analysis of stock prices and government bond yields of two major global economies using continuous wavelet transform regarding both scale and time.

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Chui, Charles K., Yu-Ting Lin, and Hau-Tieng Wu. "Real-time dynamics acquisition from irregular samples — With application to anesthesia evaluation." Analysis and Applications 14, no. 04 (April 27, 2016): 537–90. http://dx.doi.org/10.1142/s0219530515500165.

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Although most digital representations of information sources are obtained by uniform sampling of some continuous function representations, there are many important events for which only irregular data samples are available, including trading data of the financial market and various clinical data, such as the respiration signals hidden in ECG measurements. For such digital information sources, the only available effective smooth function interpolation scheme for digital-to-analog (D/A) conversion algorithms are mainly for offline applications. Hence, in order to adapt the powerful continuous-function mathematical approaches for real-time applications, it is necessary to introduce an effective D/A conversion scheme as well as to modify the desired continuous-function mathematical method for online implementation. The powerful signal processing tool to be discussed in this paper is the synchrosqueezed continuous wavelet transform (SST), which requires computation of the continuous wavelet transform (CWT), as well as its derivative, of the analog signal of interest. An important application of this transform is to extract information, such as the underlying dynamics, hidden in the signal representation. The first objective of this paper is to introduce a unified approach to remove the two main obstacles for adapting the SST approach to irregular data samples in order to allow online computation. Firstly, for D/A conversion, a real-time algorithm, based on spline functions of arbitrarily desired order, is proposed to interpolate the irregular data samples, while preserving all polynomials of the same spline order, with assured maximum order of approximation. Secondly, for real-time dynamic information extraction from an oscillatory signal via SST, a family of vanishing-moment and minimum-supported spline-wavelets (to be called VM wavelets) are introduced for online computation of the CWT and its derivative. The second objective of this paper is to apply the proposed real-time algorithm and VM wavelets to clinical applications, particularly to the study of the “anesthetic depth” of a patient during surgery, with emphasis on analyzing two dynamic quantities: the “instantaneous frequencies” and the “non-rhythmic to rhythmic ratios” of the patient’s respiration, based on a one-lead electrocardiogram (ECG) signal. Indeed, the “R-peaks” of the ECG signal, which constitute a waveform landmark for clinical evaluation, are non-uniform samples of the respiratory signal. It is envisioned that the proposed algorithm and VM wavelets should enable real-time monitoring of “anesthetic depth”, during surgery, from the respiration signal via ECG measurement.

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Santos, Celso A. G., Richarde Marques Silva, and Seyed Ahmad Akrami. "RAINFALL ANALYSIS IN KLANG RIVER BASIN USING CONTINUOUS WAVELET TRANSFORM." Journal of Urban and Environmental Engineering 10, no. 1 (August 23, 2016): 3–10. http://dx.doi.org/10.4090/juee.2016.v10n1.003010.

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The rainfall characteristics within Klang River basin is analyzed by the continuous wavelet transform using monthly rainfall data (1997–2009) from a raingauge and also using daily rainfall data (1998–2013) from the Tropical Rainfall Measuring Mission (TRMM). The wavelet power spectrum showed that some frequency components were presented within the rainfall time series, but the observed time series is short to provide accurate information, thus the daily TRMM rainfall data were used. In such analysis, two main frequency components, i.e., 6 and 12 months, showed to be present during the entire period of 16 years. Such semiannual and annual frequencies were confirmed by the global wavelet power spectra. Finally, the modulation in the 8–16-month and 256–512-day bands were examined by an average of all scales between 8 and 16 months, and 256 and 512 days, respectively, giving a measure of the average monthly/daily variance versus time, where the periods with low or high variance could be identified.

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Santos, Celso A. G., Richarde Marques Silva, and Seyed Ahmad Akrami. "RAINFALL ANALYSIS IN KLANG RIVER BASIN USING CONTINUOUS WAVELET TRANSFORM." Journal of Urban and Environmental Engineering 10, no. 1 (August 23, 2016): 3–10. http://dx.doi.org/10.4090/juee.2016.v10n1.3-10.

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The rainfall characteristics within Klang River basin is analyzed by the continuous wavelet transform using monthly rainfall data (1997–2009) from a raingauge and also using daily rainfall data (1998–2013) from the Tropical Rainfall Measuring Mission (TRMM). The wavelet power spectrum showed that some frequency components were presented within the rainfall time series, but the observed time series is short to provide accurate information, thus the daily TRMM rainfall data were used. In such analysis, two main frequency components, i.e., 6 and 12 months, showed to be present during the entire period of 16 years. Such semiannual and annual frequencies were confirmed by the global wavelet power spectra. Finally, the modulation in the 8–16-month and 256–512-day bands were examined by an average of all scales between 8 and 16 months, and 256 and 512 days, respectively, giving a measure of the average monthly/daily variance versus time, where the periods with low or high variance could be identified.

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FUJIWARA, Hisakazu, Taketoshi OKUNO, and Shigeru NISHIO. "An Example of Image Analysis with Continuous Wavelet Transform." Journal of the Visualization Society of Japan 15, Supplement1 (1995): 75–78. http://dx.doi.org/10.3154/jvs.15.supplement1_75.

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Jianqiang Gu, 谷建强, 田震 Zhen Tian, 邢岐荣 Qirong Xing, 王昌雷 Changlei Wang, 栗岩锋 Yanfeng Li, 刘丰 Feng Liu, 柴路 Lu Chai, and 王清月 Chingyue Wang. "Analysis of terahertz waveguide modes in continuous wavelet domain." Chinese Optics Letters 8, no. 11 (2010): 1057–60. http://dx.doi.org/10.3788/col20100811.1057.

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Shi, Lihua, Xinwei Wang, Gang Li, and Lingyan Zhang. "Wideband Lamb wave analysis based on continuous wavelet transform." Smart Structures and Systems 1, no. 3 (September 25, 2005): 257–66. http://dx.doi.org/10.12989/sss.2005.1.3.257.

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HSU, WEI-YEN. "CONTINUOUS EEG SIGNAL ANALYSIS FOR ASYNCHRONOUS BCI APPLICATION." International Journal of Neural Systems 21, no. 04 (August 2011): 335–50. http://dx.doi.org/10.1142/s0129065711002870.

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In this study, we propose a two-stage recognition system for continuous analysis of electroencephalogram (EEG) signals. An independent component analysis (ICA) and correlation coefficient are used to automatically eliminate the electrooculography (EOG) artifacts. Based on the continuous wavelet transform (CWT) and Student's two-sample t-statistics, active segment selection then detects the location of active segment in the time-frequency domain. Next, multiresolution fractal feature vectors (MFFVs) are extracted with the proposed modified fractal dimension from wavelet data. Finally, the support vector machine (SVM) is adopted for the robust classification of MFFVs. The EEG signals are continuously analyzed in 1-s segments, and every 0.5 second moves forward to simulate asynchronous BCI works in the two-stage recognition architecture. The segment is first recognized as lifted or not in the first stage, and then is classified as left or right finger lifting at stage two if the segment is recognized as lifting in the first stage. Several statistical analyses are used to evaluate the performance of the proposed system. The results indicate that it is a promising system in the applications of asynchronous BCI work.

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Tian, Jia. "Wavelet Analysis of Fault Diagnosis Technology." Applied Mechanics and Materials 651-653 (September 2014): 2402–5. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.2402.

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In recent years, the development of computer technology, signal processing, artificial intelligence, pattern recognition technology; and promote the continuous development of fault diagnosis technology, especially knowledge-based fault diagnosis method has been widely studied. Which, along with the increasingly improved neural network technology, the fault diagnosis method based on neural network has been widespread concern. Since one of the main steps of fault diagnosis is signal processing, while wavelet analysis is an effective tool to process signals and wavelet function has many good characteristics, so the combination of wavelet and neural network, so called wavelet neural network, has become a focus in fault diagnosis field recently.

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Didas, Stephan, and Joachim Weickert. "Integrodifferential equations for continuous multiscale wavelet shrinkage." Inverse Problems & Imaging 1, no. 1 (2007): 47–62. http://dx.doi.org/10.3934/ipi.2007.1.47.

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D'ERCOLE, ROBERTO, and JORGE MATEU. "A CONTINUOUS WAVELET-BASED APPROACH TO DETECT ANISOTROPIC PROPERTIES IN SPATIAL POINT PROCESSES." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 02 (March 2013): 1350017. http://dx.doi.org/10.1142/s0219691313500173.

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A two-dimensional stochastic point process can be regarded as a random measure and thus represented as a (countable) sum of Delta Dirac measures concentrated at some points. Integration with respect to the point process itself leads to the concept of the continuous wavelet transform of a point process. Applying then suitable translation, rotation and dilation operations through a non unitary operator, we obtain a transformed point process which highlights main properties of the original point process. The choice of the mother wavelet is relevant and we thus conduct a detailed analysis proposing three two-dimensional mother wavelets. We use this approach to detect main directions present in the point process, and to test for anisotropy.

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Ayache, Antoine, and Céline Esser. "A useful result related with zeros of continuous compactly supported mother wavelets." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 05 (August 28, 2017): 1750044. http://dx.doi.org/10.1142/s0219691317500448.

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In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More recently, they also turn out to be quite useful in the probabilistic framework of stochastic processes, in which, among other things, they allow to obtain fine results concerning erratic sample paths behavior. The goal of our paper is to derive a result, related with zeros of continuous compactly supported mother wavelets, which is useful in this probabilistic framework. More precisely, let [Formula: see text] be any arbitrary such wavelet; we show that being given an arbitrary point [Formula: see text] there always exists at least one integer [Formula: see text] such that [Formula: see text].

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Ma, Jun, Zhaoyang Wang, Minh Vo, and Bing Pan. "Wavelet selection in two-dimensional continuous wavelet transform technique for optical fringe pattern analysis." Journal of Optics 14, no. 6 (May 18, 2012): 065403. http://dx.doi.org/10.1088/2040-8978/14/6/065403.

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