scholarly journals Detection Algorithm of Particle Contamination in Reticle Images with Continuous Wavelet Transform

2001 ◽  
Author(s):  
C Chen ◽  
G Qiu
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Detection Algorithm ◽  
Continuous Wavelet ◽  
Particle Contamination

scholarly journals R Peak Detection Algorithm based on Continuous Wavelet Transform and Shannon Energy

2017 ◽  
Vol 10 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Nantarika Thiamchoo ◽  
Pornchai Phukpattaranont
Keyword(s):  
Cardiovascular Disease ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Detection Algorithm ◽  
Peak Detection ◽  
Continuous Wavelet ◽  
Qrs Complex ◽  
Peak Detection Algorithm ◽  
Shannon Energy ◽  
Ecg Data

The R peak detection algorithm is a necessary tool for monitoring and diagnosing the cardiovascular disease. This paper presents the R peak detection algorithm based on continuous wavelet transform (CWT) and Shannon energy. We evaluate the proposed algorithm with the 48 record of ECG data from MIT-BIH arrhythmia database. Results show that the proposed algorithm gives very good DER (0.48%-0.50%) compared to those from previous publications (0.168%-0.87%). We demonstrated that the use of the CWT with a single scaling parameter is capable of removing noises. In addition, we found that Shannon energy cannot improve the DER value but it can highlight the R peak from the low QRS complex in ECG beat leading to the improvement in the robustness of the R peak detection algorithm.

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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