Savitzky signal derivatives

The relative merits of these different methods can be compared by differentiating a known mathematical function. The model we will use is y = x + x /2), X = 0. .. 4, at X = 2. Various levels of noise are imposed on the signal y (Table 3.2). The resulting derivatives are shown in Table 3.3. As the noise level reduces and tends to zero, the derivative results from applying the five-point polynomial (Equation 3.4) converge more quickly towards the correct noise-free value of 3 for the first derivative, and 1 for the second derivative (Equation 3.5). As with polynomial smoothing, the Savitzky-Golay differentiation technique is available with many commercial spectrometers. 

The Savitzky-Golay filter can also be used for derivation of signal curves. For this, appropriate filter coefficients are inserted as given in Table A.7 for the first derivative and in Table A.8 for the second derivative. 

It is well known that features of signals can be enhanced by examining their derivative. Consequently, derivative cyclic voltammetry (DCV) was developed [57]. The derivative is usually calculated numerically by simple differencing (A/ /At) if the time step increments are small enough [58], by a Savitzky-Golay polynomial least-squares procedure [59], or by Fourier transformation [60]. Also, hardware based differentiation is possible [60]. 

---