Applications
- Smoothing by convolution is performed primarily for aesthetic reasons. Fitting statistical models to smoothed data is generally a mistake, since the smoothing process alters the distribution of noise.
- Location of maxima and minima in experimental data curves. The first derivative of a function is zero at a maximum or minimum.
- Location of an end-point in a titration curve. An end-point is an inflection point where the second derivative of the function is zero.
- Resolution enhancement in spectroscopy. Bands in the second derivative of a spectroscopic curve are narrower than the bands in the spectrum: they have reduced half-width. This allows partially overlapping bands to be "resolved" into separate peaks.
Read more about this topic: Numerical Smoothing And Differentiation