# Chemometrics from basick to wavelet transform - Chau F.T

ISBN 0-471-20242-8

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>B=[A A’;1.2*A sqrt(A)]

>B1=[B 3*B’;2.1*B BA2]

Finally, we have a matrix of order 16 x 16. If we key in

>plot(B1(:,9))

then Figure A.12 is generated. If we type the following statements, such as

>subplot(221),plot(B1(:,9),’*-’)

>hold

the command hold retains the current graph so that subsequent plotting commands add to the graph:

>subplot(222),plot(B1(:,10),’o-’) >subplot(223),plot(B1(:,11),’+-’) >subplot(224),plot(B1(:,11),’. — ’)

Then, Figure A.13 will appear on the screen.

If we key in the statement

>bar(B1(:,6))

we will obtain Figure A.14.

To obtain the contour plot of this data matrix, we can simply utilize the following statement.

>contour(B1)

290 appendix

Figure A.13. Plots of the ninth, tenth, and eleventh column vectors of B-i in the same graph window.

and then, we will have Figure A.15. To obtain the three-dimensional plot of the data, we can type in

>mesh(B1)

Then Figure A.16 immediately appears on the screen.

Figure A.14. Bar chart of the sixth column vector of B1.

appendix

291

Figure A.15. A contour plot of B1.

Figure A.16. A 3D mesh plot of B1.

292

appendix

For these above plots (Figs. A.12-A.16), we can still use functions such as title, xlabel, ylabel, and axis, to customize the plot such as adding a title, axis range, axis label, or other feature. In summary, the plotting functions in MATLAB are very convenient to use and make visualization of the data and results much easier and simpler.

INDEX

Ab initio calculations, wavelet transform, chemical physics and quantum chemistry, 248-249 Adaptive wavelet algorithm (AWA), classification and pattern recognition, 228 Addition, in MATLAB software: matrices, 264 vectors, 259-260 Additive measure theorem, best-basis selection, 160 All-electron density-function (AEDF) program, wavelet transform, chemical physics and quantum chemistry, 248--249 Alternative least squares (ALS),

two-dimensional signal processing, 86-87

American ginseng, chemometric analysis,

8

Analytical chemistry: chemometrics and, 6-- 8 modern developments, 1-3 multidimensional dataset, 3-5 vectors and matrices, 257--259 wavelet transform applications, 233 Approximate scale threshold, wavelet

transform, smoothing applications, 175-178

Approximation signal, packet wavelet transform, 132-134 Artificial neural network (ANN): chemometrics-based signal processing, 12

combined wavelet transform/wavelet neural network and, 230--232 wavelet transform: capillary electrophoresis, 237 classification and pattern recognition, 228

Atomic absorption spectroscopy (AAS), wavelet transform applications,

243

Atomic emission spectroscopy (AES), wavelet transform applications,

243

Background shift and removal: chemical rank, 71-75 continuous wavelet transform, 191-196 double-centered correction technique, 77-78

two-dimensional signal processing, 75--76 wavelet transform, 183-199 chromatography and capillary electrophoresis, 235-237 EXAFS spectrum, 185-191 principles and algorithms, 184 two-dimensional signals, 196-199 Baseline adjustment and removal: chemical rank, 71--75 two-dimensional signal processing, 75--76 congruence analysis and least-squares fitting, 78-80 wavelet transform, 183-199 chromatography and capillary electrophoresis, 235-237 correction techniques, 191 fast Fourier transform comparisons,

221--225 principles and algorithms, 184 Best-basis selection, wavelet packet transform, data compression, 158-166 Bilinear two-way data, 69--70 Binary tree, wavelet packet transform, data compression, 155-158 Biology, analytical chemistry and, 2-- 3 Biometrics, 5

Biorthogonal spline wavelets, 136-137 computing example, 137-140 Biorthogonal wavelet transform, 134-140 computing example, 137-140 multiresolution signal decomposition, 134-136 spline wavelets, 136--137 Bivariate function, two-dimensional wavelet transform, 140-141, 142-145 Black system, chemometrics and, 9--10 B-spline (Battle-Lemarie) wavelets,

114-116 chromatography and capillary electrophoresis, 235-237

293

294

index

curve fitting, one-dimensional signal

processing, 57-64

Calibration curve. See also

Regression/calibration combined chemometrics, 3, 8 Capillary electrophoresis (CE), wavelet transform, applications, 12, 235-237 Chemical factor analysis (CFA), 12 wavelet transform, combined techniques,

229-230

Chemical physics, wavelet transform,

248--249

Chemical rank, two-dimensional (2D) signal processing, 71--75 Chemical resolution, chemometrics and,

7-- 8

Chemometrics: defined, 3, 6

education and training in, 7-- 8 evolution of, 5-- 8 information resources: books, 12--14

mathematics software, 15--19 online resources, 14--15 technique, 2 Chromatogram simulation: wavelet packet transform: data denoising and smoothing,

180-182 resolution enhancement,

220--221 wavelet transform: background removal, two-dimensional signals, 196-199 baseline correction, 191 data denoising, 170-173 resolution enhancement, NMR spectra, 216--220

resolution enhancement, overlapping chromatograms, 212--220 smoothing, 174-178 Chromatography: two-dimensional signal processing, baseline shifting, 75--76 wavelet transform, applications,

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