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.

Research on Aeroengine Rub-Impact Fault Analysis Based on Wavelet Scalogram Statistical Feature

2011 ◽  
Vol 48-49 ◽  
pp. 942-945 ◽  
Author(s):  
Ya Hui Wu ◽  
Da Zhi Zhang ◽  
Xin Liang Li ◽  
Jing Feng Xue
Keyword(s):  
Wavelet Transform ◽  
Test Data ◽  
Continuous Wavelet Transform ◽  
Dimensional Space ◽  
Vibration Signal ◽  
Fault Analysis ◽  
Continuous Wavelet ◽  
Statistical Features ◽  
Statistical Feature

The characteristics of the continuous wavelet transform scalogram of the aeroengine vibration signal could show the fault symptomatic in the 2-dimensional space and identify the rub-impact fault of the aeroengine. In order to get the precise feature for fault analysis, the statistical features of the scalogram which incorporated the Tamura vision features were proposed to diagnose the aeroengine rub-impact faults quantitatively. The experiments on the aeroengine test data demonstrate these statistic characteristics of the scalogram effectively diagnose the rub-impact faults.

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.

Wavelet Transforms and Multirate Filtering

2002 ◽  
pp. 86-104 ◽  
Author(s):  
Raghuveer Rao
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Wavelet Transformation ◽  
Discrete Wavelet ◽  
Orthogonal Wavelet ◽  
Seminal Paper ◽  
Wavelet Expansions ◽  
Square Integrable Function ◽  
The Relationship

One of the most fascinating developments in the field of multirate signal processing has been the establishment of its link to the discrete wavelet transform. Indeed, it is precisely this link that has been responsible for the rapid application of wavelets in fields such as image compression. The objective of this chapter is to provide an overview of the wavelet transform and develop its link to multirate filtering. The birth of the field of wavelet transforms is now attributed to the seminal paper by Grossman and Morlet (1984) detailing the continuous wavelet transform or CWT. The CWT of a square integrable function is obtained by integrating it over regions defined by translations and dilations of a windowing function called the mother wavelet. The idea of representing functions or signals in terms of dilations can be found even in engineering articles dating back by several years, for example, Helstrom (1966). However, Grossman and Morlet’s formulation was more complete and was motivated by potential application to modeling seismic data. The next step of significance was the discovery of orthogonal wavelet basis functions and their role in defining multi-resolution representations (Daubechies 1988; Meyer 1992). Daubechies also provided a method for constructing compactly supported wavelets. Mallat (1989) established the fact that coefficients of orthogonal wavelet expansions can be obtained through multirate filtering which paved the way for widespread investigation of using wavelet transforms in signal and image processing applications. The objective of the chapter is to provide an overview of the relationship between multirate filtering and wavelet transformation. We begin with a brief account of the CWT, then go through the discrete wavelet transformation (DWT) followed by derivation of the relationship between the DWT and multirate filtering. The chapter concludes with an account of selected applications in digital image processing.

scholarly journals Inversion of Weinstein intertwining operator and its dual using Weinstein wavelets

2016 ◽  
Vol 24 (1) ◽  
pp. 289-307
Author(s):  
Abdessalem Gasmi ◽  
Hassen Ben Mohamed ◽  
Néji Bettaibi
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Continuous Wavelet Transforms ◽  
Intertwining Operator

Abstract In this paper, we consider the Weinstein intertwining operator ℜa, dW and its dual tR a,dW. Using these operators, we give relations between the Weinstein and the classical continuous wavelet transforms. Finally, using the Weinstein continuous wavelet transform, we deduce the formulas which give the inverse operators of R a,dW and tR a,dW.

Continuous Wavelet Transforms of Multivariable Abstract Function Spaces

2010 ◽  
Vol 159 ◽  
pp. 199-204
Author(s):  
Han Zhang Qu ◽  
Jing Yang
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Integral Kernel ◽  
Function Spaces ◽  
Continuous Wavelet ◽  
Norm Convergence ◽  
Continuous Wavelet Transforms ◽  
Abstract Function ◽  
One Dimensional ◽  
Abstract Function Spaces

An abstract function space is proposed and discussed. One-dimensional continuous wavelet transform is applied to the continuous wavelet transforms of the multivariable abstract function spaces .The reconstruction formulas of it produced by the integral kernel of the transform multivariable abstract functions and those of it produced by the integral kernel of the multivariable abstract functions which are difference from the transform multivariable abstract functions are obtained in the weak topology as well as in the sense of norm convergence.

scholarly journals Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170250 ◽  
Author(s):  
Mark P. Wachowiak ◽  
Renata Wachowiak-Smolíková ◽  
Michel J. Johnson ◽  
Dean C. Hay ◽  
Kevin E. Power ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Theme Issue ◽  
Practical Applications ◽  
Time Frequency ◽  
New Family ◽  
Physiological Processes ◽  
Analytic Wavelet

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’.

COMPLEMENTARY ANALYSIS TO HEART SOUNDS WHILE USING THE SHORT TIME FOURIER AND THE CONTINUOUS WAVELET TRANSFORMS

2007 ◽  
Vol 19 (05) ◽  
pp. 331-339
Author(s):  
S. M. Debbal ◽  
F. Bereksi-Reguig
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Continuous Wavelet Transforms ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Short Time

This paper presents the analysis and comparisons of the short time Fourier transform (STFT) and the continuous wavelet transform techniques (CWT) to the four sounds analysis (S1, S2, S3 and S4). It is found that the spectrogram short-time Fourier transform (STFT), cannot perfectly detect the internals components of these sounds that the continuous wavelet transform. However, the short time Fourier transform can provide correctly the extent of time and frequency of these four sounds. Thus, the STFT and the CWT techniques provide more features and characteristics of the sounds that will hemp physicians to obtain qualitative and quantitative measurements of the time-frequency characteristics.

scholarly journals Moment asymptotic expansions of the wavelet transforms

2017 ◽  
Vol 35 (1) ◽  
pp. 237
Author(s):  
Ashish Pathak
Keyword(s):  
Wavelet Transform ◽  
Asymptotic Expansions ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Distribution Theory ◽  
Continuous Wavelet ◽  
The Moment ◽  
Distribution Spaces

Using distribution theory we present the moment asymptotic ex-pansion of continuous wavelet transform in dierent distribution spaces for largeand small values of dilation parameter a. We also obtain asymptotic expansionsfor certain wavelet transform.

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