While research into improving data quality from analytical instrumentation has gone on for decades, only recently has research been done to improve information extraction methods. One of these methods, correlation analysis, is based upon the shifting of one function relative to another and determining a correlation value for each displacement. The cross correlation algorithm allows one to compare two files and find the similarities that exist, the convolution operation combines two functions two dimensionally (e.g. any input into an analytical instrument convolves with that instrument response to give the output) and deconvolution separates functions that have convolved together. In correlation chromatography, multiple injections are made into a chromatograph at a rate which overlaps the instrument response to each injection. Injection intervals must be set to be as random as possible within limits set by peak widths and number. When the input pattern representation is deconvolved from the resulting output, the effect of that input is removed to give the instrument response to one injection. Since the operation averages all the information in the output, random noise is diminished and signal-to-noise ratios are enhanced. The most obvious application of correlation chromatography is in trace analysis. Signal-to-noise enhancements may be maximized by treating the output data (for example, with a baseline subtraction) before the deconvolution operation. System nonstationarities such as injector nonreproducibility and detector drift cause baseline or "correlation" noise, which limit attainable signal-to-noise enhancements to about half of what is theoretically possible. Correlation noise has been used to provide information about changes in system conditions. For example, a given concentration change that occurs over the course of a multiple injection sequence causes a reproducible correlation noise pattern; doubling the concentration change will double the amplitude of each point in the noise pattern. This correlation noise is much more amenable to computer analysis and, since it is still the result of signal averaging, the effect of random fluctuations and noise is reduced. A method for simulating conventional coupled column separations by means of time domain convolution of chromatograms from single column separations is presented.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

University of Macau / Faculty of Science and Technology / Department of Mathematics

University of Macau / Faculty of Science and Technology / Department of Mathematics

Thesis (M.S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / Dr. Feodor Vainstein, Committee Member; Dr. Doug Blough, Committee Chair; Dr. David Schimmel, Committee Member. Includes bibliographical references (leaves 71-75).

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Master of Science / This project aims to develop computational tools for analyzing an underwater acoustic system designed to deter invasive fish species in the Mississippi River Basin. It leverages an established numerical framework (OpenFOAM) and deals with understanding how to model the system. The study prioritizes enhancing the accuracy of the methods developed and ways to improve its computational efficiency.

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