Filtering and Smoothing

The main purpose of smoothing a series is to strip away the random fluctuations. The analogous procedures which are used for smoothing can also be used for filtering the periodicities. Use of such techniques achieves short-term forecasts with a memory of the last values of the series. 

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Seasonal process components are of particular interest for environmental studies and production processes. The different components of x(t) can be estimated by smoothing and filtering methods. 

A. Savitsky and M. Golay, Smoothing and Filtering Functions for Analytical Data, Anal. Chem., 1964, 36, 1627-1632. 

Klein and Dratz [2] produced a 60-Hz signal with a tachometer generator, the amplitude of which was proportional to the ordinate component amplified with a lock-in amplifier, the signal was rectified, smoothed, and filtered. Only the first derivative could be generated with this method. 

In Sec. 3.6.4.1, smoothing and filtering were treated in detail. This was necessary because these operations represent the basis for the following differentiation methods. The quality of the set of data, for instance, the SNR, determines the quality as well as the suitability of derivatives. This point must be repeatedly emphasized because it is usually responsible for unsatisfactory results and artifacts. 

The following classifications concerning signal smoothing and filtering can be made ... 

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