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Brain State Identification and Forecasting of Acute Pathology Using Unsupervised Fuzzy Clustering of EEG Temporal Patterns
Published in Horia-Nicolai Teodorescu, Abraham Kandel, Lakhmi C. Jain, FUZZY and NEURO-FUZZY SYSTEMS in MEDICINE, 2017
The discrete wavelet transform of a signal can be estimated using the fast wavelet transform proposed by Mallat and Zhong [20]. At each scale, j, the wavelets’ coefficients, T2j+1f, and the smoothed signal, O2j+1S, for the next scale, j + 1, are calculated. For scale zero, j = 0, the signal, S, is used as the smoothed signal. The algorithm proposed is
Use of wavelet transform for processing of mining induced seismic events
Published in Vladimír Strakoš, Vladimír Kebo, Radim Farana, Lubomír Smutný, Mine Planning and Equipment Selection 1997, 2020
The fast wavelet transform in comparison with fast Fourier transform is even faster or extra fast. Calculation and smoothing of one signal with 4096 points on PC 486 (66 MHz) lasts about one minute including all graphical image and saving of all results. Calculation of the wavelet transform alone lasts only one second.
Spectral graph wavelet regularization and adaptive wavelet for the backward heat conduction problem
Published in Inverse Problems in Science and Engineering, 2021
The wavelet methods have been used to efficiently solve partial differential equations (PDEs) [25] due to its attractive mathematical properties which include multiscale analysis, wavelet decomposition, fast wavelet transform, vanishing moments, localization and data compression. Due to this useful properties, wavelet methods have been successfully applied to direct as well as inverse problems. For example, Haar wavelet is used by authors in [26, 27] for some direct and inverse problems. Legendre wavelets is used in [28] to solve nonlinear problems, Chebyshev and Hermite wavelet are used in [29, 30]. The numerical solution of some integral equations using wavelets based method can be seen in [31–34]. The application to some other inverse problems includes sideways heat equation [35], the Cauchy problem for the Laplace equation [36], the Cauchy problem for the Helmholtz equation [37] and backward heat conduction problem [38]. The wavelets used until now to solve inverse problems are classical wavelets which are defined on flat geometries. The critical issue is to solve the inverse problems on a general manifold and graph. The spectral graph wavelets [39] (introduced by Hammond et al. in 2011) exhibit good localization properties in the limit of fine scale. Other attractive properties include smoothness, shape-awareness, multiscale, and being flexible and adaptable for complex geometry and arbitrary topology. Moreover, in the construction of this wavelet, the mesh is not required to discretize the domain, hence is well suited for dealing with the inverse problems on general manifold and graph.
Performance improvement of machine learning models via wavelet theory in estimating monthly river streamflow
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Kegang Wang, Shahab S. Band, Rasoul Ameri, Meghdad Biyari, Tao Hai, Chung-Chian Hsu, Myriam Hadjouni, Hela Elmannai, Kwok-Wing Chau, Amir Mosavi
One of the main advantages of wavelets is that they offer simultaneous localization in the time and frequency domains. The second main advantage of wavelets is that, using a fast wavelet transform, it is possible to make calculations very quickly. Wavelets have the great advantage of being able to separate the fine details in a signal. Wavelet transform is a highly efficient mathematical transformation function in signal processing (data pre-processing) and decomposes a signal into its basic signal functions (Singh et al., 2020).
Optimized Hybrid CNN-LSTM Based Islanding Detection of Solar-Wind Power System
Published in Electric Power Components and Systems, 2023
When the current increases or decreases, the voltage changes instantaneously (in volts per second) over the given period of time. SDWTs have the advantage of being extremely fast to compute due to fast wavelet transform. The wavelet has the additional benefit of containing separate signal data. SDWT analyze several passive parameters, like ROCOV, ROCOF, and unbalanced voltage from PCC signals.