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Signal Modeling Using Spatial Filtering and Matching Wavelet Feature Extraction for Classification of Brain Activity Patterns
Published in Mridu Sahu, G. R. Sinha, Brain and Behavior Computing, 2021
Vrushali G. Raut, Sanjay R. Ganorkar, Supriya O. Rajankar, Omprakash S. Rajankar
The processing time of the discrete wavelet transform (DWT) makes it preferable in comparison with the continuous wavelet transform (CWT). The signal decomposition using DWT gives approximate and detail coefficient bands containing wavelet coefficients. It is a tool used effectively for signal compression, and the reason is an appropriate representation of the signal by removing randomness and redundancy from it [32]. The same concept of efficient representation can be used for capturing the uniqueness of the signal which will help in building robust features from the underlying activity. The beauty of this tool is in a variety of available wavelet functions for representing the signals effectively. Literature suggested the use of an empirical selection of Daubechies wavelet for the decomposition of EEG signals to give wavelet coefficients used for the preparation of features [34,35]. Thus, while using the WT, significant effort are spent on the selection of the wavelet function. This work provides the capable technique of wavelet function selection for the signal under test.
Sleep Stage Classification Using DWT and Dispersion Entropy Applied on EEG Signals
Published in Varun Bajaj, G.R. Sinha, Computer-aided Design and Diagnosis Methods for Biomedical Applications, 2021
Rajeev Sharma, Sitanshu Sekhar Sahu, Abhay Upadhyay, Rishi Raj Sharma, Ajit Kumar Sahoo
There are several methods for analyzing non-stationary signals like biomedical, earthquake, financial, and mechanical signals, etc. The wavelet transform is considered a powerful method for decomposing non-stationary signals into different scales, and provides a time-scale representation [38]. The wavelet transform is used for resolving the fixed time-frequency resolution problem of the short-time Fourier transform (STFT) [39]. The wavelet transform consists of two properties, namely space and frequency localization and multi-resolution analysis. Theoretically, the wavelet transform is broadly classified as the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). The CWT of signal y(t) is computed as follows [40]: YCWTτ,s=∫−∞∞ytψτ,s*tdt
Advanced Harmonic Analysis for Power Systems
Published in Felix Alberto Farret, Marcelo Godoy Simões, Danilo Iglesias Brandão, Electronic Instrumentation for Distributed Generation and Power Processes, 2017
Felix Alberto Farret, Marcelo Godoy Simões, Danilo Iglesias Brandão
The wavelet theory applies to many subjects. All wavelet transforms may be considered forms of time-frequency representation for continuous signals (analog), being so related to harmonic analysis. Practically, almost all discrete wavelet transforms use banks of filters in time. These filter banks are called scaling coefficients in the wavelet nomenclature and may contain filters either with a finite impulse response (FIR) or infinite impulse response (IIR). The wavelets forming a continuous wavelet transform (CWT) are subject to the principle of Fourier analysis of the uncertainty regarding the theory of sampling; i.e., given a signal with an event on it, one cannot simultaneously set a response scale in time and frequency for this event. The time response scale of all uncertainty, with regards to this particular event, has lower bandwidth. Thus, the scalogram of a continuous wavelet transform of this signal, such as an event, marks an entire region in the time-scale plan rather than of a single point. Similarly, the basis of the discrete wavelet can be considered in the context of other forms of the uncertainty principle.
Early wheel flat detection: an automatic data-driven wavelet-based approach for railways
Published in Vehicle System Dynamics, 2023
Araliya Mosleh, Andreia Meixedo, Diogo Ribeiro, Pedro Montenegro, Rui Calçada
Continuous Wavelet Transform (CWT) has been developed over the last decades, as an excellent time–frequency powerful tool to characterise local features of a signal. CWT converts the analysed signal into a set of coefficients in two dimensions [49]. Despite the Fourier transform, where the function used as the basis of the decomposition is always a sine wave, other functions can be selected for the wavelet shape according to the signal properties. The basic function in wavelet analysis is defined by two parameters: scale and translation. This feature displays several resolutions of non-stationary signals. The CWT () corresponding to the signal is defined as: where and are scale and translation parameters, respectively, and is the complex conjugate of the mother wavelet , which consists of a continuous function in both time-domain and frequency-domain. The main purpose of the mother wavelet is to provide a source function for the production of daughter wavelets, which are simply translated and scaled versions of the mother wavelet. One of the most often used mother wavelet for CWT is represented as follows: which is a Gaussian function centred on the frequency .
Extraction characteristics of pressure signals of oil pulsating flow with different particle concentration based on wavelet analysis
Published in Petroleum Science and Technology, 2022
Since the particle quantity of particle pollutants mixed in oil is a random distribution problem, the dynamic flow parameters in the time domain and frequency domain show a trend of drastic changes. The wavelet analysis can make a group of data that have good local properties in the time domain and frequency domain, the mutation information in a group of time series can be detected, and its main change periods can be analyzed; meanwhile, the influence of these periods in different periods can be obtained. Wavelet analysis mainly uses the continuous wavelet transform (CWT) to detect transient signals, and provides powerful multi-resolution in time-frequency analysis (Belaid, Miloudi, and Bournine 2021). CWT has a set of basic functions that decompose a signal into different localization levels in time and scale (Zhou et al., 2020). These operations generate wavelet coefficients through the expansion and translation of mother wavelets. Lu et al. (2017) analyzed the multi-scale decomposition of the velocity data of Particle Image Velocimetry (PIV) using the wavelet analysis method. They investigated the influence of surfactants on the turbulence characteristics of the multi-scale channels.
Applicability analysis of IR thermography and discrete wavelet transform for technical conditions assessment of bridge elements
Published in Quantitative InfraRed Thermography Journal, 2019
Leszek Różański, Krzysztof Ziopaja
Theoretical background and practical applications of Wavelet Transform were published in the early 1990s by Ingrid Daubechies, C.K. Chui, Y. Mayer and D.E. Newland. Wavelet Transform (WT) is a mathematical tool, which has been successfully used in active IR thermography [19] for the analysis of thermographic data. The main advantage of WT is its usefulness in damage identification problem solving, because it discovers and locates information in time or space on local disturbances and discontinuities in the signal that may be caused by hidden defects. Continuous wavelet transform (CWT) due to the time-consuming calculation, a very large (infinite) number of factors and because of the small number of wavelet in the analytical form, has a limited field of application in practical engineering tasks. DWT does not have the above drawbacks. In many engineering cases the analyzed one- and two-dimensional signal has a discrete form. The algorithms used for calculating the signal decomposition and reconstruction are simple and effective. The wavelets family used to DWT is large and allows to more easily choose appropriate wavelet for the specific problem. In this article, the temperature distribution (real or numeric) is treated as a set of temperature values from the area of, e.g. N = 64x64 = 4096. It means that the level of decomposition of the signal is equal to 6, which corresponds to the number of details which contain the various features of the signal. In 1989 Stephane Mallat presented the algorithm of multiresolution decomposition of two-dimensional signal F(x,y) ∊L2 in the wavelet representation: