In the omnipresent digitalization of processes, the understanding and filtering of data is becoming ever more important. Real data are usually a combination of trend and noise. Data smoothing methods help us to remove noise and reveal possible trends and patterns in the data. Many of these methods are based on local (weighted) polynomial smoothing. The thesis contains a description and solution of the general problem of local polynomial smoothing. The basic and most commonly used examples of smoothing (smoothing with polynomials of zero, first and second degree) are derived. The thesis also discusses the generalized local polynomial smoothing with weights. This is followed by a description of the moving average method, the LOWESS method, the LOESS method and the Savitzky-Golay filter. In the last part, examples are presented that demonstrate data smoothing by the considered methods on different types of data. For this purpose the implementation of the methods in the program package Matlab is used and described.
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