Spectral Analysis Methods with Continuous Wavelet Transform to Characterize Media Periodicity Using Backscattered and Simulated Ultrasound Signals

2019 ◽  
pp. 455-459
Author(s):  
Christiano Bittencourt Machado ◽  
Mahmoud Meziri ◽  
Wagner Coelho de A. Pereira ◽  
Guillermo Cortela
Keyword(s):  
Spectral Analysis ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Analysis Methods ◽  
Ultrasound Signals

scholarly journals Introduction to redundancy rules: the continuous wavelet transform comes of age

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170258 ◽  
Author(s):  
Paul S. Addison
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
State Of The Art ◽  
Structural Characteristics ◽  
Continuous Wavelet ◽  
Theme Issue ◽  
Current State ◽  
Analysis Methods ◽  
Wide Range ◽  
New Form

Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)—even when it appears most appropriate for the problem at hand—is that it is ‘redundant’. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, ‘redundant’ is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form—the CWT—is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

scholarly journals An examination of the continuous wavelet transform for volcano-seismic spectral analysis

2020 ◽  
Vol 389 ◽  
pp. 106728 ◽  
Author(s):  
Sacha Lapins ◽  
Diana C. Roman ◽  
Jonathan Rougier ◽  
Silvio De Angelis ◽  
Katharine V. Cashman ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
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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