Description This book gives an overview of the numerical data analysis and signal treatment techniques that are used in chromatography and related
separation techniques. Emphasis is given to the description of the symmetrical and asymmetrical chromatographic peak shape models. Both
theoretical and empirical models are discussed.
The fundamentals of data acquisition, types and effect of baseline noise, and methods
of improving the signal-to-noise ratio (either in time or in frequency and wavelet domain) are thoroughly discussed. Resolution enhancement
techniques, such as curve fitting, deconvolution by Fourier and wavelet transforms, iterative deconvolution, Kalman filtering and multivariate
methods of curve resolution are all discussed with several chromatographic examples. Quantitative analysis by peak area of peak height
measurement, the precision and accuracy of the quantitation of stand-alone or overlapping and symmetrical or asymmetrical peaks are treated.
In a separate chapter, guidelines are given for the use of transform techniques for the analysis of chromatograms.
A statistical description
of peak overlap is given in the final chapters. Since the concept of resolution has to be reconsidered when one separates complex mixtures,
the problem of resolution and overlap is quantitatively discussed by means of statistical methods, and by using Fourier analysis of the
complex chromatogram.
Features of this book
• The ultimate source of numerical techniques to enhance chromatographic
data
• Gives a detailed description of signal and resolution enhancement techniques in a manner applicable for enhancing not only
chromatography, but also spectroscopic and other analytical signals
• The first book with a thorough overview of the statistics
of peak overlap.
This is the first volume to encompass both the simple and more sophisticated methods for the numerical treatment of
chromatograms. It is, therefore, the fundamental resource of numerical analysis methods for every analyst.
Contents
1. Introduction. 2. Mathematical background. Random variables. Random processes. Fourier analysis.
3. Models
of chromatography. Plate models. Mass balance model. General rate model. Statistical model. Asymmetrical peak shapes. Nonlinear
chromatography. Extra-column effects. Exponentially modified Gaussian model.
4. Data acquisition. Sampling theorem.
Errors of digitalization. Recovery of the analog signal. Practical issues of sampling analytical signals. Quantitation. A/D converters.
5. Peak shape analysis. Empirical peak shape models. Curve fitting to the empirical models. Characterization of peak
asymmetry. Comparison of peak shapes.
6. Noise. Noise types and sources. The observed noise. Noise in analytical signals.
Noise profile of chromatographic detectors. Signal-to-noise ratio. Computer simulation of noise.
7. Signal enhancement.
Digital filters. Filtering in time domain. Ensemble averaging. Correlation techniques. Fourier-domain filtering. Kalman filter.
8.
Peak detection. Matched filters. Peak detection by derivatives.
9. Quantitative analysis. Graphical integration
of stand-alone peaks. Graphical integration of overlapping peaks. Numerical measurement of peak height and peak area. Accuracy and precision
of the measured values.
10 Resolution enhancement. Peak resolution. resolution of overlapping peaks. Peak sharpening.
Moment analysis of overlapping peaks. Deconvolution using natural computation.
11. Multivariate signal resolution. Factor
analysis. Spectral and chromatographic ratioing.
12. Transform techniques in chromatography. Fourier transform. Other
transforms.
13. Information theory. Entropy and information. Entropy of random variables. Information transfer through
channels. Information content of quantitative analysis. Maximum entropy method.
14. Quality assurance and validation.
Errors associated with analytical measurements. Calibration. Limit of detection. Validation of new analytical methods. Validation of
the chromatographic system.
15. Statistical theory of peak overlap. Peak resolution in multicomponent chromatograms.
Determination limit. Combinatorial analysis of peak overlap. Random retention pattern. Superposition of retention patterns. Recognition
of the retention pattern. Estimating the number of compound families. Multidimensional separations. Order-disorder in multicomponent
mixtures.
16. Fourier analysis of multicomponent chromatograms. Power spectrum of multicomponent chromatograms. Power
spectrum of a Poissonian chromatogram. Power spectrum for constant peak width. Power spectrum for varying peak width. Autocovariance function of multicomponent chromatograms. Parameter estimation. Determination of the retention pattern by Fourier analysis. Simplified
Fourier analysis. Determination of the proper sample size by Fourier analysis.
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