## 2 Materials and Methods
### Processing of the Interferogram  
The interferogram produced by the interferometer is converted mathematically (Fourier transform) into an intensity versus wavenumber plot known as a single-beam spectrum (Figure 3). The single-beam spectrum of the gas exhaust sample is ratioed (logarithmically) against the single-beam background spectrum (produced by passing nitrogen gas through the cell) to produce the absorbance spectrum [123]. Other processing of raw data (apodization) may be used to smoothen discontinuities at the beginning and end of the spectra, reduce, or eliminate noise [3; 124]. Then, to utilize the complete information of the complex spectra and to handle the large data set, multivariate analysis is often used (i.e., data analytical methods that deal with more than one variable at a time). Some combinations of variables (wavenumbers) of a given data set are highly correlated with each other. Principal component analysis (PCA) is one such widely used dimensionality reduction technique to extract the informative region of the spectra for every individual species. Unlike classification or clustering, regression is used in the quantification of particular dependent variables (expected pollutants). Some of the commonly used multivariant regression methods are classical least squares (CLS), multiple linear regression (MLR), principal component regression (PCR), partial least squares (PLS) [125]. Such calibration methods can be appropriate when the gas composition of the mixture to be analyzed (here, the exhaust gas) is not known. In that case, the compound of interest can be added to the mixture (matrix) at different concentration levels (spiking) in order to build a suitable multivariate regression model. This model might, however, highly depends on the complexity and composition of the gas mixture (matrix) used to build it. Another approach is to compare the spectra of the compound of interest to the foreseen interfering compounds (e.g., water or CO\({}_{2}\)) in order to: (i) identify the wavelength region  
Figure 3: Processing of an interferogram. where not too many interferences are expected, and (ii) identify the other wavelength regions where interferences are expected. The first region is then used to build the regression model, sometime in a straightforward way (see Figure 2b), or less straightforward way (see Figure 2c). The second set of wavelength regions will be used to foresee the possible interference brought by the compound of interest when building a regression model for other compounds. For illustration, Figure 2c shows how the N\({}_{2}\)O model is built in a wavelength area where the possible interference of CO absorption was identified. In this case, the region used to build the regression model was selected to avoid the interference of CO\({}_{2}\) and H\({}_{2}\)O (see Figure 2a). Typically, specific wavelengths where no other species absorb are used to predict the volume concentration of the compound, assuming a linear or quadratic relationship between concentration and absorption [28; 47; 118]. For each compound, standard gas cylinders of several concentration levels are used to calibrate the model. Such an approach has the advantage of being more robust and less dependent on the composition of the mixture. However, this approach requires to be exhaustive in consideration of the expected interferences, thus having a library including the pure spectra of all the compounds expected to be found in vehicle exhaust. Once the regression model is built, analysis of the spectral residual is also a crucial step in order to identify potential interfering compounds in the models created. It is important to highlight that the reference spectra must be recorded at the same conditions, meaning the same instrument (same optical system, including optical path), and same temperature and pressure as used for the exhaust measurements [126; 127].