Numerical Manipulation of Digitized Curves

There are different reasons for the numerical manipulation of data. One of these is data reduction others are filtering and smoothing, magnification of the amplitude of the spectra or of certain spectral features, and standardization. After the preceding computations, different algorithms for digital differentiation can be applied. 

Generally, the smoothed ordinate of the /th data point is a function of n (=2 m + 1) non-smoothed equidistant points yi and of the coefficients Cj,  

In the normal sliding average, is a constant, and in the weighted average Ci becomes linearly or nonlinearly (exponentially) smaller. 

Without any smoothing, even moderate background noise can cause a jagged structure in the derivatives, which makes any quantitative evaluation impossible. On the other hand, extensive smoothing eliminates the characteristics of some low-intensity peaks. Note All smoothing operations will demand a compromise between SNR and resolution. 

When Ck is zero and A 0, one-sided smoothing occurs. Only previous data points are considered (Fig. 3-46d). The coefficient drops exponentieilly with A 0, and this digital filter has the mode of action of an RC-analog filter. Since data points in the past and in the future are treated differently, - the signal is distorted. 

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