scholarly journals An asymptotic expansion of continuous Wavelet transform for large dilation parameter

2018 ◽  
Vol 36 (3) ◽  
pp. 27-39
Author(s):  
Ashish Pathak ◽  
Prabhat Yadav ◽  
M. M. Dixit
Keyword(s):  
Asymptotic Expansion ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Special Cases ◽  
Morlet Wavelet Transform

In this paper , we derive asymptotic expansion of the wavelet transform for large values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Mexican Hat wavelet and Morlet wavelet transform are obtained as a special cases.

scholarly journals Asymptotic Expansions of the Wavelet Transform for Large and Small Values ofb

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
R. S. Pathak ◽  
Ashish Pathak
Keyword(s):  
Wavelet Transform ◽  
Asymptotic Expansions ◽  
Fourier Transforms ◽  
Haar Wavelet ◽  
Haar Wavelet Transform ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Special Cases ◽  
Morlet Wavelet Transform ◽  
Translation Parameter

Asymptotic expansions of the wavelet transform for large and small values of the translation parameterbare obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values ofbwhen asymptotic expansions of the function and the wavelet near origin are given.

scholarly journals On alternative wavelet reconstruction formula: a case study of approximate wavelets

2014 ◽  
Vol 1 (2) ◽  
pp. 140124 ◽  
Author(s):  
Elena A. Lebedeva ◽  
Eugene B. Postnikov
Keyword(s):  
Wavelet Transform ◽  
Wide Class ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Physical Processes ◽  
Admissibility Condition ◽  
Oscillatory Dynamics

The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.

scholarly journals Damping identification in multi-degree-of-freedom systems using the continuous wavelet transform

2005 ◽  
Vol 27 (1) ◽  
pp. 41-50 ◽  
Author(s):  
Nguyen Phong Dien
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Damping Ratio ◽  
Morlet Wavelet ◽  
Wavelet Function ◽  
Degree Of Freedom ◽  
Damping Coefficient ◽  
Steel Beam ◽  
Continuous Wavelet ◽  
Modal Damping

The identification of damping in multi-degree-of-freedom vibration systems is a well-known problem and appears to be of crucial interest. Compared to an estimation of the stiffness and mass, the damping coefficient or, alternatively, damping ratio is the most difficult quantity to determine. In this paper, the continuous wavelet transform based on the Morlet-wavelet function is used to identify the modal damping ratios of multi-degree-of-freedom vibration systems. A new wavelet-based method for the damping identification from measured free responses is presented. The proposed method was also tested by experiments on a steel beam.

scholarly journals A wavelet neural control scheme for a quadrotor unmanned aerial vehicle

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170248 ◽  
Author(s):  
F. Jurado ◽  
S. Lopez
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Unmanned Aerial Vehicle ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Wavelet Neural Network ◽  
Continuous Wavelet ◽  
Continuous Wavelets ◽  
Control Scheme ◽  
Aerial Vehicle

Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time–frequency plane. The Gaussian, the Mexican hat and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using the continuous wavelet transform. Continuous wavelets are favoured when high temporal and spectral resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of a recurrent high-order neural network model, a novel wavelet neural network structure, here called a recurrent Morlet wavelet neural network, is proposed in order to achieve a better identification of the behaviour of dynamic systems. The effectiveness of our proposal is explored through the design of a decentralized neural backstepping control scheme for a quadrotor unmanned aerial vehicle. The performance of the overall neural identification and control scheme is verified via simulation and real-time results. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

Defects Diagnosis of Bearing by Means of Acoustic Emission and Continuous Wavelet Transform

2009 ◽  
Vol 413-414 ◽  
pp. 651-657 ◽  
Author(s):  
Ru Jiang Hao ◽  
Zhi Peng Feng ◽  
Fu Lei Chu
Keyword(s):  
Acoustic Emission ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Rolling Bearing ◽  
Morlet Wavelet ◽  
Wavelet Function ◽  
Continuous Wavelet ◽  
Test Rig ◽  
Ae Signal ◽  
Transform Coefficients

The acoustic emission signals of rolling bearing with different type of defects are de-noised and illustrated by the continuous wavelet transform and scalogram. Morlet wavelet function is selected and the wavelet parameters are optimized based on the principle of minimal wavelet entropy. The soft-threshold de-noising is used to filter the wavelet transform coefficients. The de-noised signals obtained by reconstructing the wavelet coefficients show the obvious impulsive features. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the real AE signal from the defective rolling bearing in experimental test rig. The results indicate that the proposed method is useful and efficient for signal purification and features extraction.

Sign in / Sign up

Export Citation Format

Share Document