Hazards of Digital Smoothing Filters as a Preprocessing Tool in Multivariate Calibration

The efficacy of smoothing first-order data as a preprocessing method for multivariate calibration is discussed. In particular, the use of symmetric smoothing filters (such as Savitzky–Golay filters) is examined from the perspective of calibration performance, in contrast with past studies based on univariate signal-to-noise improvement. It is shown mathematically that in the limit of a perfect calibration model (i.e. all the errors derive from the measurement uncertainty in the unknown sample), no gains in multivariate calibration performance can be made by the application of symmetric smoothing filters. The proof is corroborated by simulated multivariate calibration procedures, namely principal component regression (PCR). Real experimental data are also used, yielding similarly supportive evidence in favor of the theoretical result. On occasion, marginal performance enhancements (less than a factor of two) are observed in both the simulated and real data. The conditions under which these enhancements are likely to occur are discussed. The recently introduced multivariate calibration technique of maximum likelihood PCR (MLPCR) is also applied using the measurement error covariance information determined from the applied filter matrix. MLPCR is shown to be invariant in calibration performance, even under extreme filtering conditions. Copyright  1999 John Wiley & Sons, Ltd.