Signal Processing of Displacement Interferometer Based on the Continuous Wavelet Transform

2008 ◽  
Vol 35 (8) ◽  
pp. 1235-1239 ◽  
Author(s):  
刘寿先 Liu Shouxian ◽  
李泽仁 Li Zeren ◽  
吴建荣 Wu Jianrong ◽  
王德田 Wang Detian ◽  
刘俊 Liu Jun ◽  
...  
Keyword(s):  
Signal Processing ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet

A New Application of Continuous Wavelet Transform to Overlapping Chromatograms for the Quantitative Analysis of Amiloride Hydrochloride and Hydrochlorothiazide in Tablets by Ultra-Performance Liquid Chromatography

2012 ◽  
Vol 95 (3) ◽  
pp. 751-756 ◽  
Author(s):  
Erdal Dinç ◽  
Eda Büker
Keyword(s):  
Signal Processing ◽  
Wavelet Transform ◽  
Quantitative Analysis ◽  
Continuous Wavelet Transform ◽  
Standard Addition ◽  
Ultra Performance Liquid Chromatography ◽  
Continuous Wavelet ◽  
Constant Flow Rate ◽  
Acquity Uplc ◽  
Amiloride Hydrochloride

Abstract A new application of continuous wavelet transform (CWT) to overlapping peaks in a chromatogram was developed for the quantitative analysis of amiloride hydrochloride (AML) and hydrochlorothiazide (HCT) in tablets. Chromatographic analysis was done by using an ACQUITY ultra-performance LC (UPLC) BEH C18 column (50 × 2.1 mm id, 1.7 μm particle size) and a mobile phase consisting of methanol–0.1 M acetic acid (21 + 79, v/v) at a constant flow rate of 0.3 mL/min with diode array detection at 274 nm. The overlapping chromatographic peaks of the calibration set consisting of AML and HCT mixtures were recorded rapidly by using an ACQUITY UPLC H-Class system. The overlapping UPLC data vectors of AML and HCT drugs and their samples were processed by CWT signal processing methods. The calibration graphs for AML and HCT were computed from the relationship between concentration and areas of chromatographic CWT peaks. The applicability and validity of the improved UPLC-CWT approaches were confirmed by recovery studies and the standard addition technique. The proposed UPLC-CWT methods were applied to the determination of AML and HCT in tablets. The experimental results indicated that the suggested UPLC-CWT signal processing provides accurate and precise results for industrial QC and quantitative evaluation of AML-HCT tablets.

A new paradigm for signal processing of Raman spectra using a smoothing free algorithm: Coupling continuous wavelet transform with signal removal method

2013 ◽  
Vol 44 (4) ◽  
pp. 608-621 ◽  
Author(s):  
Ahmad Esmaielzadeh Kandjani ◽  
Matthew J. Griffin ◽  
Rajesh Ramanathan ◽  
Samuel J. Ippolito ◽  
Suresh K. Bhargava ◽  
...  
Keyword(s):  
Signal Processing ◽  
Wavelet Transform ◽  
Raman Spectra ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
New Paradigm ◽  
Removal Method

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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