The design of a novel mother wavelet that is tailor-made for continuous wavelet transform in extracting defect-related features from reflected guided wave signals

Measurement ◽  
2017 ◽  
Vol 110 ◽  
pp. 176-191 ◽  
Author(s):  
Jingming Chen ◽  
Javad Rostami ◽  
Peter W. Tse ◽  
Xiang Wan
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Guided Wave ◽  
Continuous Wavelet ◽  
Mother Wavelet

scholarly journals Continuous wavelet transform on local fields

2015 ◽  
Vol 34 (2) ◽  
pp. 113-121 ◽  
Author(s):  
Ashish Pathak
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Local Fields ◽  
Continuous Wavelet ◽  
Mother Wavelet ◽  
Basic Properties

The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution are also studied.

The continuous wavelet transform with rotations

2005 ◽  
Vol 4 (1) ◽  
pp. 45-55
Author(s):  
Jaime Navarro ◽  
Miguel Angel Alvarez
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet

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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