$$L^p$$–$$L^q$$ time-scale localization operator for the continuous Hankel wavelet transform

2020 ◽  
Vol 11 (3) ◽  
pp. 1367-1388
Author(s):  
C. Baccar ◽  
A. Kabache ◽  
F. Meherzi
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Localization Operator

Pattern Changes of Time-Shifted Vibration Signals on Wavelet Time-Scale Maps

1995 ◽  
Author(s):  
Da Jun Chen ◽  
Wei Ji Wang
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Wavelet Transforms ◽  
Vibration Signal ◽  
Continuous Wavelet ◽  
Time Axis ◽  
Orthogonal Wavelet ◽  
Signal Component ◽  
Analysis Technique ◽  
Map Analysis

Abstract As a multi-resolution signal decomposition and analysis technique, the wavelet transforms have been already introduced to vibration signal processing. In this paper, a comparison on the time-scale map analysis is made between the discrete and the continuous wavelet transform. The orthogonal wavelet transform decomposes the vibration signal onto a series of orthogonal wavelet functions and the number of wavelets on one wavelet level is different from those on the other levels. Since the grids are unevenly distributed on the time-scale map, it is shown that a representation pattern of a vibration component on the map may be significantly altered or even be broken down into pieces when the signal has a shift along the time axis. On contrary, there is no such uneven distribution of grids on the continuous wavelet time-scale map, so that the representation pattern of a vibration signal component will not change its shape when the signal component shifts along the time axis. Therefore, the patterns in the continuous wavelet time-scale map are more easily recognised by human visual inspection or computerised automatic diagnosis systems. Using a Gaussian enveloped oscillation wavelet, the wavelet transform is capable of retaining the frequency meaning used in the spectral analysis, while making the interpretation of patterns on the time-scale maps easier.

Adaptive carrier fringe pattern enhancement for wavelet transform profilometry through modifying intrinsic time-scale decomposition

2020 ◽  
Vol 59 (20) ◽  
pp. 6191
Author(s):  
Hanxiao Wang ◽  
Yinghao Miao ◽  
Hailu Yang ◽  
Zhoujing Ye ◽  
Linbing Wang
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Fringe Pattern ◽  
Intrinsic Time ◽  
Time Scale Decomposition

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

scholarly journals Wavelet Transform in Vibration Analysis for Mechanical Fault Diagnosis

1996 ◽  
Vol 3 (1) ◽  
pp. 17-26 ◽  
Author(s):  
W.J. Wang
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Vibration Signals ◽  
Time Frequency ◽  
Special Cases ◽  
Mechanical Faults ◽  
Short Time

The wavelet transform is introduced to indicate short-time fault effects in associated vibration signals. The time-frequency and time-scale representations are unified in a general form of a three-dimensional wavelet transform, from which two-dimensional transforms with different advantages are treated as special cases derived by fixing either the scale or frequency variable. The Gaussian enveloped oscillating wavelet is recommended to extract different sizes of features from the signal. It is shown that the time-frequency and time-scale distributions generated by the wavelet transform are effective in identifying mechanical faults.

scholarly journals Wavelet application in acoustic emission signal detection of wire related events in pipeline

2021 ◽  
Author(s):  
Ran Wu
Keyword(s):  
Signal Processing ◽  
Acoustic Emission ◽  
Wavelet Transform ◽  
Signal Detection ◽  
Time Scale ◽  
Inspection Time ◽  
Time Frequency ◽  
Pipeline Inspection ◽  
Ae Signal ◽  
Thesis Work

This thesis establishes an automatic classification program for the signal detection work in pipeline inspection. Time-scale analysis provides the basic methodology of this thesis work. The wavelet transform is implemented in the program for filtering out the majority of noise and detect needed signals. As a popular nondestructive test, acoustic emission (AE) testing has been widely used in many physical and engineering fields such as leak detection and pipeline inspection. Among those applied AE tests, a common problem is to extract the physical features of the ideal events, so as to detect similar signals. In acoustic signal processing, those features can be represented as joint time frequency distribution. However, classical signal processing methods only give global information on either time or frequency domain, while local information is lots. Although the short-time Fourier transform (STFT) is developed to analyze time and frequency details simultaneously, it can only achieve limited precision. Other time-frequency methods are also applied in AE signal processing, but they all have the problem of resolution and time consuming. Wavelet transform is a time-scale technique with adaptable precision, which makes better feature extraction and detail detection. This thesis is an application of wavelet transform in AE signal detection where various noise exists. The wavelet transform with Morelet wavelet as the mother wavelet provides the basis of the program for auto classification in this thesis work. Finally the program is tested with two industrial projects to verify the workability of wavelet transforms and the reliability of the developed auto classifiers.

Multi-time scale analysis of runoff at the Yangtze estuary based on the Morlet Wavelet Transform method

2014 ◽  
Vol 11 (6) ◽  
pp. 1499-1506 ◽  
Author(s):  
Cui-ping Kuang ◽  
Ping Su ◽  
Jie Gu ◽  
Wu-jun Chen ◽  
Jian-le Zhang ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Yangtze Estuary ◽  
Morlet Wavelet ◽  
Scale Analysis ◽  
The Yangtze Estuary ◽  
Transform Method ◽  
Morlet Wavelet Transform

Early Detection of Fatigue Damage on Rolling Element Bearings Using Adapted Wavelet

2007 ◽  
Vol 129 (4) ◽  
pp. 495-506 ◽  
Author(s):  
Xavier Chiementin ◽  
Fabrice Bolaers ◽  
Jean-Paul Dron
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Degrees Of Freedom ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Mechanical Shock ◽  
Vibratory Analysis ◽  
Rolling Element ◽  
Shock Response

Among the advanced techniques of the predictive maintenance, the vibratory analysis proves to be very effective, in particular, for monitoring rotating components such as the bearings. Their damage creates cyclic efforts which are at the origin of the processing of vibratory measurements. This processing can be made by temporal methods, frequential methods, or by time-scale methods using the wavelets for 2 decades. The wavelet transform is a very effective processing, however, the difficulties of application and interpretation of the results slow down their employment. The determination of the parameters of the wavelets makes its use all the more difficult. Moreover, the use of these time-scale methods is very expensive in time computation. This paper proposes a wavelet adapted to the mechanical shock response of a structure with n degrees of freedom. In addition, we developed a procedure for analysis of signals by this wavelet which makes it possible to accelerate the process and to improve detection in the case of disturbed signals. This methodology is compared with the traditional time-scale methods and is implemented to detect defects of different sizes on outer rings and inner rings of ball bearings.

scholarly journals CLUSTERING FUNCTIONAL DATA USING WAVELETS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350003 ◽  
Author(s):  
ANESTIS ANTONIADIS ◽  
XAVIER BROSSAT ◽  
JAIRO CUGLIARI ◽  
JEAN-MICHEL POGGI
Keyword(s):  
Wavelet Transform ◽  
Similarity Measure ◽  
Functional Data ◽  
Time Scale ◽  
Clustering Algorithms ◽  
Input Function ◽  
Wavelet Coherence ◽  
High Dimensional ◽  
Feature Selection Technique ◽  
Homogeneous Groups

We present two strategies for detecting patterns and clusters in high-dimensional time-dependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand.

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