Savitzky-Golay filter smoothing using

Polynomials do not play an important role in real chemical applications. Very few chemical data behave like polynomials. However, as a general data treatment tool, they are invaluable. Polynomials are used for empirical approximations of complex relationships, smoothing, differentiation and interpolation of data. Most of these applications have been introduced into chemistry by Savitzky and Golay and are known as Savitzky-Golay filters. Polynomial fitting is a linear, fast and explicit calculation, which, of course, explains the popularity. 

Figure 6.4 The influence of spectral resolution (RES) and zero-filling factor (ZFF) on the detectability of IR spectral features of colon tissue. In this example, identical positions of a tissue sample mounted on a CaF2 window of a thickness of 1 mm were characterised by utilising a Bruker IR Scope II IR microscope. Transmission type IR spectra were recorded using a circular aperture of 900 pm diameter and a Cassegrain objective (36 x, NA 0.5, SR ca. 25 pm). A Happ-Genzel apodization function and a first derivative Savitzky-Golay filter with nine smoothing points were applied to the spectra.

Figure 6.5 Spectral features as a function of the apodisation function in mid-IR microspectroscopy of tissues (colon tissue cryo-section, same sample position as in Figure 6.4). Transmission type spectra were acquired using Bruker s IRScope II microscope and an IFS28/B spectrometer. Further measurement parameters aperture diameter 900 pm, Cassegrain objective (36 x, NA 0.5), 128 scans, optical substrate CaF2 pm of 1 mm thickness. Spectral resolution 6 cm zero-filling factor (ZFF) 4. Transmission spectra were processed with a first derivative Savitzky-Golay filter with nine smoothing points.

Methods used for preliminary examination of the data included smoothing the spectral data, multiplicative scatter correction, standard normal variance correction, baseline correction, and first- or second-derivative transformation of log (1/T) data. The smoothing and derivative transformations were based on the Savitzki-Golay second-order polynomial filter (22). 

We have carried out simulations using polynomial least-squares filters of the type described by Savitzky and Golay (1964) to determine the impact of such smoothing on apparent resolution. For quadratic filters, a filter length of one-fourth of the linewidth (at FWHM) does not seriously degrade the apparent resolution of two Gaussian lines in very close proximity. 

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