REPORT each gasoline sample. Much work, however, should be done to verify t h a t the calibration step uses a valid experimental design. Ideally, each chemical component should vary ind e p e n d e n t l y over a b r o a d r a n g e within the calibration model. PCR, then, can determine how many principal components are necessary to span the measurement space and accurately predict the octane number. When done definitively, this experimental design phase can be nearly as laborious as the CLS method. We should point out that preprocessing data using mean-centering (4, 13) or derivative (1, 13) methods often results in improved SEP values. In particular, for xylene quantitation using PCR, the SEP for all isomers can be reduced to below 0.50% if one takes the second derivative of the xylene m e a s u r e m e n t s prior to principal components analysis and regression. The second derivative removes irreproducible i n s t r u m e n t a l baseline offsets and slopes from the spectra. Because our purpose here was to explain and critically compare digital filtering and multivariate regression, rather than to estimate xy-
lene concentrations with minimal error, we have omitted further discussion of data preprocessing.
Summary We have described the similarities and differences between finite impulse response digital filtering and multivariate regression as they pertain to quantitative property estimation. These techniques formulate a filter that operates on an input measurement to give a desired state variable estimate as an output. Bialkowski has shown that selection of the correct filter is based on one's knowledge of the signal and noise characteristics (2). He showed that if the signal and the noise are precisely known, either matched filtering (random noise only) or the KIF (both random and cyclic noise) methodologies optimally filter the data. Although this is true, caution should be used when following this logic. If something in the system is not perfectly understood and modeled when the filter is constructed, errors may result in property estimation. Furthermore, these filtering methods are not useful for the case commonly encoun-
tered in q u a n t i t a t i v e a n a l y s i s in which a complete understanding of the system is not at hand. We have shown that multivariate regression provides a powerful recipe for designing finite impulse response f i l t e r s , which a c c u r a t e l y e x t r a c t properties from data contaminated with both random and cyclic noise. PCR uses a statistically designed c a l i b r a t i o n e x p e r i m e n t to c r e a t e property extraction filters and therefore does not require a full understanding of the signals and noise a priori. The calibration step of PCR requires only t h a t an independent reference method determine the properties of the component(s) of interest, but great care must be taken to assure that the calibration model spans the variance of the other components in the data. Unlike the KIF and CLS, inverse regression techniques can predict properties t h a t depend on multiple components in the system. Xylene concentrations, properties t h a t depend only on the individual component signals, were estimated to compare the methods. The KIF, CLS, and PCR methods were all capable of es-
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ISCO CIRCLE 50 ON READER SERVICE CARD 1162 A · ANALYTICAL CHEMISTRY, VOL. 64, NO. 24, DECEMBER 15, 1992
