Smoothing of data

Description of Tables -1.4 Evaluation, Selection, and Smoothing of Data... 

In computer programs that are now devoted to these problems the interpolation and smoothing of data are special cases of convolution of the data with a set of numerical coefficients, represented for the present by the vector A)data points are entered as a vector y ( /), the convolution can be written in the form... 

Rate Data. Figure 1-b shows typical rate profiles for the formation and depletion of the major species present in the excess air flames as represented by Flame A. The rates are computer generated and reflect, in some cases, an over-magnification of small deviations in the original data, mainly associated with the mole fraction profiles. Additional smoothing of data would improve the continuity of the curves, but overall, the trends and relative rate values would remain about the same. 

Very efficient smoothing of data is obtained with filters that weight the raw data differently. In the case of the moving-average filter, all the data were weighted by the same factor, that is, l/(2m -I-1) (cf. Eq. (3.1)). A better fit results if weights are used that... 

Fig. 11. Desmearing of data Fit of Ii (m) (see Fig. 10 and Eq. (35)) by cubic splines. The inset shows the smoothing of data at high q whereas the fit of the data at low q amounts to an interpolation...

Evaluation, Selection and Smoothing of Data 1.4.1 Assignment of Uncertainties... 

---