Page 37 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

P1: GJB Revised Pages
Encyclopedia of Physical Science and Technology En001f25 May 7, 2001 13:58

576 Analytical Chemistry

currently developing with the advent of parallel process- processing, resultant conversion, and information organi-
ing and neural networks for interactive “learning.” zation. Software packages for these purposes are commer-
cially available.

3. Fourier Transform Analysis
1. Common Chemometric Methods
One application of high-speed computers to data anal-
ysis is often found in spectrophotometric applications, The three most commonly used chemometric methods are
such as infrared and nuclear magnetic resonance tech- discussed in the following subsections.
niques. Samples can be irradiated with broad ranges of
frequencies from the appropriate regions of the electro- Multiple regression analysis. This is suitable for
magnetic spectrum and will absorb certain discrete fre- data modeling and expresses data as a simple equation.
quencies dependent on sample chemistry. Each indepen- The process begins with experimentation to produce a vec-
dent frequency that can be observed (resolved) in the range tor of measured data known as the “dependent” variables.
of energies employed can be represented as a sinusoidal Then a limited number of “factors” are considered to be
oscillation. The simultaneous superpositioning of all the significant for the determination of data values, and these
available frequencies produces both constructive and de- “independent” variables are used to prepare a model for
structive interference, resulting in a well-defined complex the data. Finally, coefficients, as shown below, are calcu-
waveform pattern. Interaction of the sample with discrete latedbyleast-squaresanalysistorepresentthesignificance
frequencies will alter the waveform pattern, which will or weighting of the independent variables. The result is a
then contain the analytical interaction information in the calculation of “regression coefficients” to prepare a math-
form of a time “domain.” This can be converted to a con- ematical model that is suitable for preditions,
ventional frequency-domain spectrum by the fast Fourier d = c 1 i 1 + c 2 i 2 +· · · + c n i n ,
transform algorithm, so that individual frequencies that
make up the superimposed waveform can be individually where d represents the dependent variable, c represents
identified and plotted in conventional formats. Data must the regression coefficient, andi represents the independent
be sampled and digitized at a rate at least twice the value of variable.
the ratio of the range of frequencies encountered divided
by the frequency resolution desired. The major advantage Factor analysis. This method is used to interpret
of this technique is that all frequencies are simultaneously underlying factors responsible for data and is one of the
measured, and a complete conventional spectrum can be most versatile chemometric methods. Factor analysis pro-
constructed in seconds for any one measurement. Since vides a purely mathematical model prepared from abstract
these spectra are digitized and contain frequency refer- values, which are related to a data matrix as follows,
ence information, it is possible to sum sequential spectra D = RC,
to improve signal-to-noise ratio. Signals increase linearly
where D represents the data matrix and R and C represent
with spectral addition, while noise increases as the square
factors for each row and column. The factors are math-
root of the number of spectra that are combined.
ematically transformed so that their significance can be
interpreted with respect to the data. This results in the es-
B. Chemometrics tablishment of the number of significant factors and assists
in the correlation of data and the application of physical
The term chemometrics describes the interface between
significance to the factors.
analytical chemistry and applied mathematics, where
mathematical and statistical methods are employed to
Pattern recognition. This procedure allows the
maximize information quality in a chemical experiment.
classification of a species to be made on the basis of a
Most chemometric methods involve matrix algebra, which
series of measurements that establish a pattern. Proce-
is efficiently handled by computer, and numerous pro-
durally, a matrix describing the patterns of a number of
grams are presently available. A number of reviews have
species is constructed. Then a decision vector is designed
been written on this broad subject area, which includes
by the use of standards to divide the patterns into discrete
such topics as statistics, modeling and parameter esti-
classifications, resulting in a mathematical form,
mation, resolution, calibration, signal processing, image
analysis, factor analysis, pattern recognition, optimization
p = V 1 d 1 + V 2 d 2 +· · · + V n d n ,
strategies, and artificial intelligence. Appropriate topics
can be chosen to optimize an analysis at each level of where p represents a set of patterns, V represents com-
experimentation, including sampling, measurement, data ponents of the decision vector, and d represents the data