*3.2. Savitzky–Golay Convolution Smoothing*

Savitzky–Golay (SG) convolutional smoothing, also known as polynomial smoothing [27], was proposed by Savitzky and Golay. The SG convolution smoothing method is currently a relatively widely used spectral filtering method. The smoothing method combines a least-squares fitting with a moving window. First, a window with an odd number of points is taken. Then, each point of the spectrum in the window is taken as a polynomial. Finally, least square method is used to fit the polynomial coefficient value. The formula is defined as follows:

$$\chi\_{\rm k,smooth} = \frac{1}{\rm H} \sum\_{\rm i=-W}^{+\rm W} \chi\_{\rm k+i} \mathbf{h}\_{\rm i} \tag{1}$$

where hi is a smooth coefficient and can be obtained by polynomial fitting. H is a normalization factor and the calculation method is H <sup>=</sup> <sup>+</sup> w i=−w hi.
