scholarly journals Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 522
Author(s):  
Jaime Navarro-Fuentes ◽  
Salvador Arellano-Balderas ◽  
Oscar Herrera-Alcántara
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Local Convergence ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
The Space Lp

The smoothness of functions f in the space Lp(R) with 1<p<∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.

ON-LINE HEALTH MONITORING AND DAMAGE DETECTION OF STRUCTURES BASED ON THE WAVELET TRANSFORM

2008 ◽  
Vol 08 (03) ◽  
pp. 367-387 ◽  
Author(s):  
B. ZHU ◽  
A. Y. T. LEUNG ◽  
C. K. WONG ◽  
W. Z. LU
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Discrete Wavelet Transform ◽  
Health Monitoring ◽  
Continuous Wavelet Transform ◽  
Abrupt Change ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Random Decrement Technique ◽  
On Line

Presented herein is an experiment that aims to investigate the applicability of the wavelet transform to damage detection of a beam–spring structure. By burning out the string that is connected to the cantilever beam, high-frequency oscillations are excited in the beam–spring system, and there results an abrupt change or impulse in the discrete-wavelet-transformed signal. In this way, the discrete wavelet transform can be used to recognize the damage at the moment it occurs. In the second stage of damage detection, the shift of frequencies and damping ratios is identified by the continuous wavelet transform so as to ensure that the abrupt change or impulse in the signal from the discrete wavelet transform is a result of the damage and not the noise. For the random forced vibration, the random decrement technique is used on the original signal to obtain the free decaying responses, and then the continuous wavelet transform is applied to identify the system parameters. Some developed p version elements are used for the parametric studies on the first stage of health monitoring and to find the damage location. The results show that the two-stage method is successful in damage detection. Since the method is simple and computationally efficient, it is a good candidate for on-line health monitoring and damage detection of structures.

Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform

2011 ◽  
Vol 462-463 ◽  
pp. 461-466 ◽  
Author(s):  
Shahrum Abdullah ◽  
S.N. Sahadan ◽  
Mohd Zaki Nuawi ◽  
Zulkifli Mohd Nopiah
Keyword(s):  
Wavelet Transform ◽  
Data Analysis ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Data Extraction ◽  
Morlet Wavelet ◽  
Analysis Time ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Fatigue Data

The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

Improving Space Localization Properties of the Discrete Wavelet Transform

Informatica ◽  
2013 ◽  
Vol 24 (4) ◽  
pp. 657-675
Author(s):  
Jonas Valantinas ◽  
Deividas Kančelkis ◽  
Rokas Valantinas ◽  
Gintarė Viščiūtė
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Discrete Wavelet ◽  
Space Localization

An Adaptive Binarization Method for Cost-efficient Document Image System in Wavelet Domain

2020 ◽  
Vol 64 (3) ◽  
pp. 30401-1-30401-14 ◽  
Author(s):  
Chih-Hsien Hsia ◽  
Ting-Yu Lin ◽  
Jen-Shiun Chiang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Document Image ◽  
Background Information ◽  
Raspberry Pi ◽  
Discrete Wavelet ◽  
Image System ◽  
Low Frequencies ◽  
Cost Efficient ◽  
Binarization Method

Abstract In recent years, the preservation of handwritten historical documents and scripts archived by digitized images has been gradually emphasized. However, the selection of different thicknesses of the paper for printing or writing is likely to make the content of the back page seep into the front page. In order to solve this, a cost-efficient document image system is proposed. In this system, the authors use Adaptive Directional Lifting-Based Discrete Wavelet Transform to transform image data from spatial domain to frequency domain and perform on high and low frequencies, respectively. For low frequencies, the authors use local threshold to remove most background information. For high frequencies, they use modified Least Mean Square training algorithm to produce a unique weighted mask and perform convolution on original frequency, respectively. Afterward, Inverse Adaptive Directional Lifting-Based Discrete Wavelet Transform is performed to reconstruct the four subband images to a resulting image with original size. Finally, a global binarization method, Otsu’s method, is applied to transform a gray scale image to a binary image as the output result. The results show that the difference in operation time of this work between a personal computer (PC) and Raspberry Pi is little. Therefore, the proposed cost-efficient document image system which performed on Raspberry Pi embedded platform has the same performance and obtains the same results as those performed on a PC.

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