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Chemometrics from basick to wavelet transform - Chau F.T

Chau F.T Chemometrics from basick to wavelet transform - Wiley publishing , 2004. - 333 p.
ISBN 0-471-20242-8
Download (direct link): chemometricsfrombasics2004.pdf
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246--247 MathCAD software, chemometrics applications, 17 Mathematica, chemometrics applications,
17
Mathematical microscope,
chemometrics-based signal processing, wavelet transform,
11--12 Mathematics: analytical chemistry and, 2-- 3 in MATLAB software, 276--278 Mathematics software, chemometrics and wavelet transform, 15--19 MATLAB software:
basic principles, 273--292 chemometrics and wavelet transform,
16
data compression, fast wavelet transform, 153-154 fast Fourier transform, 50 finite discrete signal handling, wavelet transform, symmetrization operation, 127 graphic functions, 288--291 linear algebra principles, 257--273 mathematical functions, 276--278 matrix construction, 275 matrix manipulation, 275 matrix subscript system, 280--286 Savitsky-Golay filter smoothing, 28--32 simple difference numerical differentiation, 54--55 spline smoothing, 37--39 symbols and notation, 274 vector and matrix generation,
278--280
vector and matrix operations, 257--292 wavelet function applications, 114 Matrices, 257--292
3GG
index
analytical chemistry, 257-259 construction, 275 decomposition, 286-288 derivatives, 271 determinants, 265-266 eigenvalues and eigenvectors,
268-269 generalized inverse, 270-271 generating methods, 278-280 inverse of, 266 manipulation of, 275 multiplication, 264 operations, 263-264 orthogonal matrix, 266-267 singular-value decomposition, 269-270 square matrix trace, 267-268 subscript system, 280-286 transposes of, 265 zero and identity matrices, 264 Measurement data matrix, chemical rank,
71--75
Median absolute deviation (MAD), wavelet transform: data denoising, 167 spectroscopy applications, 238--243 Meyer wavelet function, 113-114 Minimum description length (MDL) criterion, wavelet transform data compression, threshold determination, 162 Minitab software, chemometrics applications, 18 MINMAX thresholding, wavelet transform: chromatogram simulation, 170-173 data denoising, 167-170 spectroscopy applications, 238--243 Model residuals, chemical rank, principal components analysis, 72--75 Moore-Penrose inverse, defined,
270--271 Morlet wavelet basis function: chromatography and capillary electrophoresis, 235--237 combined wavelet transform/wavelet neural network, 232 Mother wavelets, wavelet transform, 101-108
Moving-window average smoothing: evolving factor analysis, 89--90 finite discrete signal handling, wavelet transform, 126-132 one-dimensional signaling, 24--25 wavelet transform, conventional methods comparisons, 182-183
Moving-window polynomial least-squares fitting, one-dimensional signal processing, 55--57 Multichannel measurement,
one-dimensional signaling, spectroscopy and Hadamard transformation, 41--44 Multidimensional datasets, basic principles, 3-- 5
Multidimensional wavelet analysis, two-dimensional wavelet transform, 140-141 Multiple linear regression (MLR), wavelet transform, 225--227 Multiplication, matrices, 264 Multiresolution signal decomposition (MRSD) algorithm: biorthogonal spline wavelets, 136-137 biorthogonal wavelet transform, 134-136 B-spline (Battle-Lemarie) wavelets,
114-116 fast wavelet transform, 119-122 Haar wavelet, 102-108, 113 packet wavelet transform, 133-134 wavelet transform, 102-113 chemical physics and quantum chemistry, 248 resolution enhancement, 212-220 spectroscopy, 238--243 Multivariate calibration: chemometrics and, 7-- 8 instrumental response, 8-- 9 Multivariate statistical process control (MSPC), wavelet transform, spectroscopic applications,
242--243 MuPAD software, chemometrics applications, 18
Near-infrared (NIR) spectroscopy, wavelet transform, 24G--243 Net analytical signal, two-dimensional signal processing, local principal-component analysis (PCA) and rankmap, 83--85 Neural networks: chemometrics and, 7-- 8 wavelet neural network (WNN), 12 Noise level estimation: analytical chemistry vectors and matrices, 257--259 two-dimensional signal processing,
75--76
index
301
Noise thresholds, chemical rank, principal components analysis, 72-75 Noisy analytical signals: combined wavelet transform/chemical factor analysis, 229-230 discrete wavelet transform, derivative calculation, 202-205 Fourier transformation, 50-52 Savitsky-Golay filter, 27-32 Nuclear magnetic resonance (NMR) spectrum: continuous wavelet transform (CWT), background removal, 192-196 wavelet transform: applications, 242-243 data compression, 162-166 resolution enhancement, overlapping spectra, 216-220 Numerical differentiation: analytical chemistry and, 3 continuous wavelet transform, 205--210 one-dimensional signal processing,
54--57
moving-window polynomial
least-squares fitting method,
55--57
simple difference method, 54--55 two-dimensional data, 80-81 wavelet transform resolution enhancement: comparison of methods, 210-211 discrete wavelet transform, 200--205 Nyquist critical frequency, wavelet
transform, smoothing applications, 175-178
One-dimensional (1D) signal processing: data compression, 57--67 B-spline curve fitting, 57--64 Fourier transformation, 64 principle-component analysis, 64--67 digital smoothing and filtering techniques,
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