Examples of wavelet transform in analytical signal processing

Note: Most of the programs were developed based on WaveLab 7.0. WaveLab is a toolbox developed by WaveLab Development Team (Jonathan Buckheit, Shaobing Chen, David Donoho, Iain Johnstone, and Jeffrey Scargle) in Stanford University, and it can be downloaded from http://www-stat.stanford.edu/~wavelab/. Instructions for installation are also available in the web site. You must install the WaveLab before running these programs.

• ex01 - Compression of a simulated signal using FWT
• ex02 - Compression of a simulated signal using WPT
• ex03 - Data compression of an experimental NMR spectrum
• ex04 - Denoising of a simulated chromatogram
• ex05 - Data smoothing of a simulated chromatogram
• ex06 - Data smoothing of an experimental chromatogram
• ex07 - Denoising and smoothing of the simulated and the experimental chromatograms using WPT
• ex08 - Background removal of an EXAFS spectrum
• ex09 - Large spectral line removal of a simulated NMR spectrum
• ex10 - Approximate derivative calculation of simulated signals by using DWT
• ex11 - Approximate derivative calculation of simulated signals by using CWT
• ex12 - Resolution enhancement of an overlapping chromatogram by using the Method A
• ex13 - Resolution enhancement of an overlapping NMR spectrum by using the Method B

Click all examples for the zipped TAR files.

References:

[1] Foo-tim Chau, Yi-zeng Liang, Junbin Gao, Xue-guang Shao, Chemometrics: From Basics to Wavelet Transform, Wiley-Interscience, Hoboken, New Jersey. 2004.

[2] Xueguang Shao, Alexander Kai-Man Leung, Foo-Tim Chau, Wavelet: a new trend in chemistry,Accounts of Chemical Research, 2003, 36 (4):276-283

[3] Xueguang Shao, Wensheng Cai, Wavelet Analysis in Analytical Chemistry,Reviews in Analytical Chemistry, 1998, XVII(4), 235-285

[4] Limin Shao, Xiangqin Lin, Xueguang Shao, Wavelet Transform and Its Applications in Spectroscopic Analysis, Applied Spectroscopy Reviews, 2002, 37(4):429-450

[5] Xueguang Shao, Wensheng Cai, Peiyan Sun, Maosen Zhang, Guiwen Zhao, Quantitative Determination of the Components in Overlapping Chromatographic Peaks Using Wavelet Transform, Analytical Chemistry, 1997,69(9):1722-1725

[6] Xueguang Shao, Limin Shao, Guiwen Zhao, Extraction of Extended X-ray Absorption Fine Structure Information from the Experimental Data Using the Wavelet Transform, Analytical Communications, 1998, 35(4):135-137

[7] Xueguang Shao, Wensheng Cai, Resolution of multicomponent chromatograms by window factor analysis with wavelet transform preprocessing, Journal of Chemometrics, 1998,12(2):85-93

[8] Xueguang Shao, Wensheng Cai, Peiyan Sun, Determination of component number in the overlapping multicomponent chromatogram using wavelet transform, Chemometrics and Intelligent Laboratory Systems, 1998, 43:147-155

[9] Xueguang Shao, Wensheng Cai, Zhongxiao Pan, Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis, Chemometrics and Intelligent Laboratory Systems, 1999, 45(1-2):249-256

[10] Xueguang Shao, Wan Li, Gang Chen, Qingde Su, On-line analysis of the photoacoustic spectral signal using wavelet transform, Fresenius Journal of Analytical Chemistry, 1999, 363(3):215-218

[11] Xueguang Shao, Wensheng Cai, A novel algorithm of the wavelet packets transform and its application to de-noising of analytical signals, Analytical Letters, 1999, 32(4):743-760

[12] Xueguang Shao, Shuquan Hou, On-line resolution of overlapping chromatograms using the wavelet transform, Analytical Sciences, 1999, 15:681-684

[13] Xueguang Shao, Fang Yu, Hongbing Kou, Cai Wensheng, Zhongxiao Pan, A wavelet-based genetic algorithm for compression and de-noising of chromatograms, Analytical Letters, 1999, 32(9):1899-1915

[14] Xueguang Shao, Shuquan Hou, An on-line wavelet transform for de-noising of high performance liquid chromatograms, Analytical Letters, 1999,32(12):2507-2520

[15] Xueguang Shao, Chunyan Pang, Shouguo Wu, Xiangqin Lin, Development of wavelet transform voltammetric analyzer, Talanta, 2000, 50(6):1175-1182

[16] Xueguang Shao, Hua Gu, Jihui Wu, Yunyu Shi, Resolution of the NMR spectrum using wavelet transform, Applied Spectroscopy, 2000, 54(5):731-738

[17] Xueguang Shao, Chunyan Pang, Qingde Su, A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform, Fresenius Journal of Analytical Chemistry, 2000, 367(6):525-529

[18] Wensheng Cai, Liya Wang, Zhongxiao Pan, Jian Zuo, Cunyi Xu, Xueguang Shao, Application of wavelet transform in quantitative analysis of Raman spectrum, Journal of Roman Spectroscopy, 2001, 32(3):207-209

[19] Xueguang Shao, Li Sun, An application of the continuous wavelet transform to resolution of multicomponent overlapping analytical signals, Analytical Letters, 2001, 34(2): 267-280

[20] Xueguang Shao, Chaoxiong Ma, Application of adaptive wavelet algorithm to the resolution and quantitative analysis of overlapping multicomponent chromatogram, Analytical Letters, 2003, 36(6):1261-1277

[21] Xueguang Shao, Chaoxiong Ma, A general approach to derivative calculation using wavelet transform, Chemometrics and Intelligent Laboratory Systems, 2003, 69(1-2):157-165

[22] Xueguang Shao, Yadong Zhuang, Determination of chlorogenic acid in plant samples by using near-infrared spectrum with wavelet transform preprocessing, Analytical Sciences, 2004, 20(3):451-454

[23] Chaoxiong Ma, Xueguang Shao, Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra, Journal of Chemical Information and Computer Sciences, 2004, 44(3):907-911