FREQUENCY RESPONSE OF NORRIS GAP DERIVATIVES AND ITS PROSPERITIES FOR GAS SPECTRA ANALYSIS
The article deals with an analysis of the properties of Norris gap derivatives. It discusses issues related to determining information from optical spectra measured with spectrometers. Impulse responses of differentiating filters were introduced using both Norris and Savitzky-Golay methods. The amplitude-frequency responses of the first and second order Norris differentiating filters were compared. The length impact of both segment and gaps on the frequency characteristics of filters was compared. The processing of exemplary gas spectra using the discussed technique was subsequently presented. The effect of first and second order derivatives on the spectra of carbon monoxide rotational lines for low resolution measurements is investigated. The Norris method of derivatives are very simple to implement and the calculation of their parameters does not require the use of advanced numerical methods.
Norris method; optical spectra derivative; spectroscopy; signal processing
Brown C. D., Vega-Montoto L., Wentzell P. D.: Derivative preprocessing and optimal corrections for baseline drift in multivariate calibration. Applied Spectroscopy 54(7), 2000, 1055–1068. DOI: https://doi.org/10.1366/0003702001950571
Candan Ç., Inan H.: A unified framework for derivation and implementation of Savitzky–Golay filters. Signal Processing 104, 2014, 203–211. DOI: https://doi.org/10.1016/j.sigpro.2014.04.016
Dai W., Selesnick I., Rizzo J. R., Rucker J., Hudson T.: A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades. Journal of vision 17(9), 2017, 10–19. DOI: https://doi.org/10.1167/17.9.10
Davies A. M. C.: Derivative? What Do You Mean “Derivative”? NIR news 4(4), 1993, 10–11. DOI: https://doi.org/10.1255/nirn.199
De Jong S. A., O'Brien W. L., Lu Z., Cassidy B. M., Morgan S. L., Myrick M. L.: Optimization of gap derivatives for measuring blood concentration of fabric using vibrational spectroscopy. Applied Spectroscopy 69(6), 2015, 733–748. DOI: https://doi.org/10.1366/14-07693
Figueiredo N. S., Ferreira L. H., Dutra O. O.: An Approach to Savitzky-Golay Differentiators. Circuits, Systems, and Signal Processing 38(9), 2019, 4369–4379. DOI: https://doi.org/10.1007/s00034-019-01045-w
Giakas G., Baltzopoulos V.: Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives. Journal of biomechanics 30(8), 1997, 851–855. DOI: https://doi.org/10.1016/S0021-9290(97)00043-2
Gorry P. A.: General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Analytical Chemistry 62(6), 1990, 570–573. DOI: https://doi.org/10.1021/ac00205a007
Hopkins D. W.: What is a Norris derivative?. NIR news 12(3), 2001, 3–5. DOI: https://doi.org/10.1255/nirn.611
Hopkins D.W.: Revisiting the Norris derivative quotient math in regression. NIR news 27(7), 2016, 23–28. DOI: https://doi.org/10.1255/nirn.1643
Kennedy H. L.: Improving the frequency response of Savitzky-Golay filters via colored-noise models. Digital Signal Processing 102, 2020, 102743. DOI: https://doi.org/10.1016/j.dsp.2020.102743
Kus S., Marczenko Z., Obarski N.: Derivative UV-VIS spectrophotometry in analytical chemistry. Chem. Anal 41(6), 1996, 889–927
Lee L. C., Liong C. Y., Jemain A. A.: A contemporary review on Data Preprocessing (DP) practice strategy in ATR-FTIR spectrum. Chemometrics and Intelligent Laboratory Systems 163, 2017, 64–75. DOI: https://doi.org/10.1016/j.chemolab.2017.02.008
Luo J., Ying K., He P., Bai J.: Properties of Savitzky-Golay digital differentiators. Digital Signal Processing 15(2), 2005, 122–136. DOI: https://doi.org/10.1016/j.dsp.2004.09.008
Pan T., Zhang J., Shi X.: Flexible vitality of near-infrared spectroscopy – Talking about Norris derivative filter. NIR news 31(1-2), 2020, 24–27. DOI: https://doi.org/10.1177/0960336019889587
Pasquini C.: Near infrared spectroscopy: A mature analytical technique with new perspectives – A review. Analytica Chimica Acta 1026, 2018, 8–36. DOI: https://doi.org/10.1016/j.aca.2018.04.004
Savitzky A., Golay M. J.: Smoothing and differentiation of data by simplified least squares procedures. Analytical chemistry 36(8), 1964, 1627–1639. DOI: https://doi.org/10.1021/ac60214a047
Van Veen E. H., de Loos-Vollebregt M. T. C.: Application of mathematical procedures to background correction and multivariate analysis in inductively coupled plasma-optical emission spectrometry. Spectrochimica Acta Part B: Atomic Spectroscopy 53(5), 1998, 639–669.
Wulf M., Staude G., Knopp A., Felderhoff T.: Efficient design of FIR filter based low-pass differentiators for biomedical signal processing. Current Directions in Biomedical Engineering 2(1), 2016, 215–219. DOI: https://doi.org/10.1515/cdbme-2016-0048
Yang Y., Pan T., Zhang J.: Global optimization of Norris derivative filtering with application for near-infrared analysis of serum urea nitrogen. American Journal of Analytical Chemistry 10(5), 2019, 143–152. DOI: https://doi.org/10.4236/ajac.2019.105013
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