On the Baire Generic Validity of the t-Multifractal Formalism in Besov and Sobolev Spaces by Moez Ben Abid, Mourad Ben Slimane, Ines Ben Omrane, Borhen Halouani

“…The (p,t)-oscillation exponent is measured by determining to which oscillation spaces Op,ts (defined in terms of wavelet coefficients) f belongs. In this paper, we first prove embeddings between oscillation and Besov-Sobolev spaces. …”
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A Joint Encryption and Reversible Data Hiding Scheme Based on Integer-DWT and Arnold Map Permutation by Shun Zhang, Tiegang Gao, Guorui Sheng

“…The cover image is transformed to the frequency domain with integer discrete wavelet transform (integer DWT) for the encryption and data hiding. …”
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Spectral Analysis of the Svalbard Temperature Record 1912–2010 by Ole Humlum, Jan-Erik Solheim, Kjell Stordahl

“…By means of Fourier and wavelet analysis the record is decomposed into time-frequency space, to extract information on periodic signals and their amplitude and variation over time. …”
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Study on Missing Data Filling Algorithm of Nuclear Power Plant Operation Parameters by Tianshu Wang, Ren Yu, Qiao Peng

“…Firstly, to locate the missing data accurately the detecting algorithm for missing data of the NPP operation parameters based on wavelet analysis. Different judging basis is proposed for discrete and continuous missing respectively. …”
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Field Measurement and Energy Analysis of Ground-Borne Vibration around High-Speed Railway Viaduct by Yanmei Cao, Qi Xiang, Boyang Li, Zhaoyang Li

“…Besides the independent time domain and frequency domain analysis, the continuous wavelet transform (CWT) is performed on the vibration signal to analyze the energy distribution characteristics of ground vibrations from the view of time-frequency synchronous analysis. …”
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Research on Wheel-Rail Local Impact Identification Based on Axle Box Acceleration by Yuanjin Ji, Junwei Zeng, Wenjing Sun

“…Additionally, to address mode aliasing produced during empirical mode decomposition (EMD) used in classical HHT, this study proposed to first use complete EMD with adaptive noise for the decomposition of original vibration data, then eliminate the trend-term components with the calculated correlation coefficients, and finally perform denoising on high-frequency noisy components using the wavelet threshold method. After weighted reconstruction using denoised high-frequency components and low-frequency information components, data processing was finally optimized via HHT. …”
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Instantaneous Frequency Identification Using Adaptive Linear Chirplet Transform and Matching Pursuit by Chang Xu, Cong Wang, Jingbo Gao

“…The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes. A wavelet-based identification method is simulated to compare with the proposed method, with the comparison results showing that the chirplet-based method is effective and accurate in identifying both time-varying and closely spaced frequencies. …”
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Accuracy of the Photometric Redshifts of Brightest Cluster Galaxies Identified in the CFHTLS-W1 by Sinan Aliş

“…BCGs were identified from the galaxy cluster sample produced by the Wavelet Z Photometric (WaZP) cluster finding algorithm between $0.1 < z < 1$. …”
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The Vibration Characteristics of Ground of Rock Blasting in Silt-Rock Strata by Tao Yin, Chuanbo Zhou, Changqing Zheng, Jugen Fu, Ziru Guo

“…According to the measured data of blasting vibrations at the sites, the waveform duration of vibration acceleration and the distribution characteristics of dominant frequency of vibration velocity were analyzed, the energy characteristics of vibration velocity were researched by wavelet analysis, and the attenuation laws of vibration velocity were studied by dimensional analysis (DA). …”
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Mining Outlier Data in Mobile Internet-Based Large Real-Time Databases by Xin Liu, Yanju Zhou, Xiaohong Chen

“…Upon local characteristic time scale parameters of information flow, the phase position features of the outlier data before filtering are obtained; the decision-tree outlier-classification feature-filtering algorithm is adopted to acquire signals for analysis and instant amplitude and to achieve the phase-frequency characteristics of outlier data. Wavelet transform threshold denoising is combined with signal denoising to analyze data offset, to correct formed detection filter model, and to realize outlier data mining. …”
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Spatial Spectroscopy Approach for Detection of Internal Defect of Component without Zero-Position Sensors by Qizhou Wu, Yong Jin, Zhaoba Wang, Zhaoqian Xiao

“…Specifically, the spatial variation wave of distance between the detecting source and object surface is analyzed, from which a periodical cycle is determined with the correlative approaches. Additionally, a wavelet method is adopted to reduce the noise of the periodic distance signal. …”
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An Efficient Noise Elimination Method for Non-stationary and Non-linear Signals by Averaging Decomposed Components by Zhenzhou Sun, Hongchao Lu, Jiefeng Chen, Jialong Jiao

“…A non-stationary signal and a non-linear signal are selected to investigate the performance of the proposed method, the results show that the proposed method has better de-noising efficiency compared with the wavelet shrinkage method and the Savitzky–Golay filter method based on EMD (EMD-SG) for dealing with the signals with SNR of 10 dB, 15 dB, and 20 dB, and de-noised signal using the proposed method has the highest signal-to-noise ratio (SNR) and the least root mean square error (RMSE).…”
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Fault Diagnosis of Train Axle Box Bearing Based on Multifeature Parameters by Xiaofeng Li, Limin Jia, Xin Yang

“…In the first part, a db4 wavelet is employed for denoising the original signals from the vibration sensors. …”
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A New Pipeline for Snooping Keystroke Based on Deep Learning Algorithm by Massimo Orazio Spata, Valerio Maria Russo, Alessandro Ortis, Sebastiano Battiato

“…To address this issue, mathematical wavelet transforms have been tested, while key recognition has been implemented using the inference test of a deep learning model based on a Temporal Convolutional Network (TCN). …”
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Pattern Recognition of the Vertical Hydraulic Fracture Shapes in Coalbed Methane Reservoirs Based on Hierarchical Bi-LSTM Network by Zhaozhong Yang, Chenxi Yang, Xiaogang Li, Chao Min

“…Then we present a hierarchical Bidirectional LSTM (Bi-LSTM) network to recognize the pattern of hydraulic fracture geometry in CBM reservoirs. Inputting the wavelet denoised sequences of data to the presented network, we can extract the implicit features of the hydraulic sand fracturing operation curves and automatically combine them to make the classification of the fracture shapes. …”
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Damage Identification of Piles Based on Vibration Characteristics by Xiaozhong Zhang, Wenjuan Yao, Bo Chen, Dewen Liu

“…Then the technology of computational analysis of wavelet transform was used to damage identification for pile. …”
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Evaluation on Filter Performance of Variational Mode Decomposition and Its Application in Separating Closely Spaced Modes by Wenjing Gu, Li Zhou

“…Compared with the noise-assisted versions of empirical mode decomposition (EMD) and wavelet packet transform (WPT), the parameter-optimized VMD can successfully separate the closely spaced modes while recovering the most modal information simultaneously. …”
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Dynamic Responses of the Metro Train’s Bogie Frames: Field Tests and Data Analysis by Xuhui He, Kehui Yu, Chenzhi Cai, Yunfeng Zou

“…Then, the soft thresholding process and discrete wavelet transform decomposition process are conducted to obtain a denoised version of the original signals in the time-frequency domain. …”
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A New Transferable Fault Diagnosis Approach of Rotating Machinery Based on Deep Autoencoder and Dominant Features Selection under Different Operating Conditions by Fei Dong, Xiao Yu, Xinguo Shi, Ke Liu, Zhaoli Wu, Wanli Yu

“…First, maximal overlap discrete wavelet packet transform is applied for signals processing and mix-domains statistical feature extraction. …”
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Rural Acoustic Landscape Analysis Based on Segmentation and Extraction of Spectral Image Feature Information by Huijun Xiao, Tangsen Huang, Ensong Jiang

“…In this article, the Gabor wavelet filtering method is proposed to filter and analyze the spectral image. …”
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