A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

2000 ◽  
Vol 367 (6) ◽  
pp. 525-529 ◽  
Author(s):  
X. Shao ◽  
C. Pang ◽  
Q. Su
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Photoacoustic Spectrum ◽  
Approximate Derivative ◽  
Novel Method

Approximate Derivative Calculated by Using Continuous Wavelet Transform

2002 ◽  
Vol 42 (2) ◽  
pp. 274-283 ◽  
Author(s):  
Lei Nie ◽  
Shouguo Wu ◽  
Xiangqin Lin ◽  
Longzhen Zheng ◽  
Lei Rui
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Approximate Derivative

scholarly journals A Novel Method to Estimate the Damage Severity Using Spatial Wavelets and Local Regularity Algorithm

2020 ◽  
Vol 14 (54) ◽  
pp. 36-55
Author(s):  
Mallikarjuna Reddy ◽  
Arun Kumar K
Keyword(s):  
Wavelet Transform ◽  
Mode Shape ◽  
Continuous Wavelet Transform ◽  
Structural Damage ◽  
Damage Identification ◽  
Local Regularity ◽  
Beam Model ◽  
Continuous Wavelet ◽  
Novel Method ◽  
Shape Data

 In the process of structural damage detection using continuous wavelet transform (CWT), the perturbation or damage is located by identifying the defects locally in the input signal data.  In this work the damage identification procedure using continuous wavelet transform is developed. This method is studied numerically using a simple beam model. The influence of reduced spatial sampling using fundamental mode shape is investigated in detail. The method is also investigated to ascertain the smallest level of damage identified using strain energy mode shape data.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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