Wavelet Analysis: Mother Wavelet Selection Methods

Wavelet analysis, being a popular time-frequency analysis method has been applied in various fields to analyze a wide range of signals covering biological signals, vibration signals, acoustic and ultrasonic signals, to name a few. With the capability to provide both time and frequency domains information, wavelet analysis is mainly for time-frequency analysis of signals, signal compression, signal denoising, singularity analysis and features extraction. The main challenge in using wavelet transform is to select the most optimum mother wavelet for the given tasks, as different mother wavelet applied on to the same signal may produces different results. This paper reviews on the mother wavelet selection methods with particular emphasis on the quantitative approaches. A brief description of the proposed new technique to determine the optimum mother wavelet specifically for machinery faults diagnosis is also presented in this paper.

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Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform

Journal of Applied Mechanics ◽

10.1115/1.2896009 ◽

1995 ◽

Vol 62 (4) ◽

pp. 841-846 ◽

Cited By ~ 126

Author(s):

Kikuo Kishimoto ◽

Hirotsugu Inoue ◽

Makoto Hamada ◽

Toshikazu Shibuya

Keyword(s):

Wavelet Transform ◽

Frequency Analysis ◽

Gabor Wavelet ◽

Flexural Wave ◽

Lateral Impact ◽

Dispersive Waves ◽

Time Frequency Analysis ◽

Arrival Times ◽

Time Frequency ◽

Wide Range

A new approach is presented for investigating the dispersive character of structural waves. The wavelet transform is applied to the time-frequency analysis of dispersive waves. The flexural wave induced in a beam by lateral impact is considered. It is shown that the wavelet transform using the Gabor wavelet effectively decomposes the strain response into its time-frequency components. In addition, the peaks of the time-frequency distribution indicate the arrival times of waves. By utilizing this fact, the dispersion relation of the group velocity can be accurately identified for a wide range of frequencies.

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Research on Goniometer Fault Detection of a Certain Missile Based on Wavelet Analysis

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.490-495.1600 ◽

2012 ◽

Vol 490-495 ◽

pp. 1600-1604

Author(s):

Zhu Lin Wang ◽

Jiang Kun Mao ◽

Zi Bin Zhang ◽

Xi Wei Guo

Keyword(s):

Wavelet Transform ◽

Wavelet Analysis ◽

Discrete Wavelet Transform ◽

Frequency Analysis ◽

Discrete Wavelet ◽

Analysis Method ◽

Frequency Method ◽

Time Frequency Analysis ◽

Time Frequency ◽

Fault Characteristic

Aiming at the problem of existing time-frequency analysis methods was not effective to goniometer keeping fault of a certain missile, combined time -frequency analysis method of CWT and DWT for the fault was put forward based on the fault characteristic. The process of the method proposed was given and the time-frequency method of continuous and discrete wavelet transform was analysed. The signal when goniometer keeping fault occurred was analysed by the method that was put forward. The simulation showed that the method which was effective to the fault detecting could accurately detect the time and location of goniometer fault occurred.

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Joint Time-Frequency And Wavelet Analysis - An Introduction

Metrology and Measurement Systems ◽

10.2478/mms-2014-0054 ◽

2014 ◽

Vol 21 (4) ◽

pp. 741-758 ◽

Cited By ~ 7

Author(s):

Andrzej Majkowski ◽

Marcin Kołodziej ◽

Remigiusz J. Rak

Keyword(s):

Wavelet Analysis ◽

Frequency Analysis ◽

Fourier Spectrum ◽

Frequency Content ◽

Short Time Fourier Transform ◽

Time Frequency Analysis ◽

Time Frequency ◽

Stationary Signals ◽

Frequency Window ◽

Short Time

Abstract A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.

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ELAN: A Software Package for Analysis and Visualization of MEG, EEG, and LFP Signals

Computational Intelligence and Neuroscience ◽

10.1155/2011/158970 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11 ◽

Cited By ~ 74

Author(s):

Pierre-Emmanuel Aguera ◽

Karim Jerbi ◽

Anne Caclin ◽

Olivier Bertrand

Keyword(s):

Frequency Analysis ◽

Software Package ◽

Signal Analysis ◽

Large Data ◽

Multidimensional Analysis ◽

Spatiotemporal Resolution ◽

Time Frequency Analysis ◽

Time Frequency ◽

Strong Trend ◽

Wide Range

The recent surge in computational power has led to extensive methodological developments and advanced signal processing techniques that play a pivotal role in neuroscience. In particular, the field of brain signal analysis has witnessed a strong trend towards multidimensional analysis of large data sets, for example, single-trial time-frequency analysis of high spatiotemporal resolution recordings. Here, we describe the freely available ELAN software package which provides a wide range of signal analysis tools for electrophysiological data including scalp electroencephalography (EEG), magnetoencephalography (MEG), intracranial EEG, and local field potentials (LFPs). The ELAN toolbox is based on 25 years of methodological developments at the Brain Dynamics and Cognition Laboratory in Lyon and was used in many papers including the very first studies of time-frequency analysis of EEG data exploring evoked and induced oscillatory activities in humans. This paper provides an overview of the concepts and functionalities of ELAN, highlights its specificities, and describes its complementarity and interoperability with other toolboxes.

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