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Example For Designing Digital Filters

WindDataSuite implements a module for designing digital low-pass, high-pass, band-pass, and inverse band-pass filters. The filter kinds comprise running mean, ideal rectangular filter, and Lanczos cosine filter. In the following example, low-pass filters have been designed for a cut-off period (50% energy pass) of 24 values (measuring intervals). When the sampling rate of the measurement is 10 minutes then this corresponds to a cut-off period of 4 hours .
The figures of the filter response show, that the running mean has a very bad filter response: bad energy pass in the cut-off transition zone and beyond, and phase inversions at periods less than the cut-off period (Fig.1) - also in the case that the filter factors nearly match the correct energy pass at the cut-off period (Fig.2). Despite of its very bad filter response, WindDataSuite also provides the running mean as a digital filter since it is still used widely .
The ideal rectangular filter matches the cut-off energy pass very well, but still shows phase inversions and energy amplifications (Gibbs oscillations) in the vicinity of the cut-off period transition band (Fig.3).
The Lanczos cosine filter minimizes the Gibbs oscillation and shows a very good filter response (Fig.4).

Abb. FilDes1 Abb. FilDes2
Fig.1: Running mean with 25 filter factors Fig.2: Running mean with 15 filter factors
Abb. FilDes3 Abb. FilDes4
Fig.3: Ideal rectangular filter Fig.4: Lanczos cosine filter
 
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Computing time : approx. 1 second
Processing time : approx. 1 minute