*3.1. Signal Processing*

To quickly process the measurement data for this project, we applied the Savitzky– Golay filter method [32] for signal smoothing and differentiation. This digital filtering technique fits successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. As a result of this moving-window data smoothing process, it increased the precision of the data without distorting the signal tendency. Another important aspect of this Savitzky–Golay filtering technique is that it also obtains derivative information of the signal profile based on the fitted polynomials. For spectroscopy applications, the Savitzky–Golay filtering technique can help to reduce signal noise and identify structure components in complex spectra [33,34]. It enables us to achieve fast numerical

data analysis of recorded measurement transmission absorption spectra for determining gas concentrations in gas sensing applications.

Figure 3a shows one example of a CO2 measurement spectrum and the associated 1st and 2nd derivatives obtained via a Savitzky–Golay filtering. The transmission spectrum was acquired for samples of ~500 ppmv CO2 by the ADC with 450 data points, and averaged 16 times in successive laser current scans. Simulations of the absorbance and 2nd differentiation spectrum at 1 ppmv CO2 concentration are displayed in Figure 3b. The 16 bits ADC for recording the photodetector signal has sufficient resolution (i.e., 1/65,535) to cover concentrations from ~2000 ppmv down to sub ppmv. Our noise-limited detection sensitivity corresponds to an absorbance level of ~1.5 × <sup>10</sup><sup>−</sup>4.

**Figure 3.** (**a**) A measurement example of tunable diode laser transmission spectrum of CO2 absorption, and the subsequent numerical analysis of its transmission-intensity-normalized 1st and 2nd differentiations by Savitzky–Golay filtering; (**b**) simulations of absorbance and 2nd differentiation at 1 ppmv CO2 concentration.
