Geopsy: Filter
Filter is a Basic signal processing tool in the Waveform menu and a tab in some advanced signal processing tools. In the first case, it applies a filter to the signals in the active signal viewer. In the second case, it applies a filter to the active signals for various purposes as detailed for each particular tool.
In Waveform menu, by clicking on Filter, a pop-up window appears to customize the filter. In that case Filter modifies the temporary signals in the active viewer.
Filter parameters
The basic parameters for the filter is the type of filter:
- Low pass filters the frequencies above a given value.
- High pass filters the frequencies below a given value.
- Band pass filters the frequencies out of a given frequency range.
- Band reject filters the frequencies inside a given frequency range.
The cut-off frequency(ies) of the filter should be provided in the neighboring text box(es). All the values are in Hertz.
Filter method
Two filters are currently implemented in Geopsy.
Butterworth filter
Butterworth filter is linear continuous-time filter with a maximally flat frequency response. By default, the filter is applied in both directions that makes it non-outphasing but not causal (filter output depends also on inputs in time). The Causal checkbox ensures the filter will be causal (filter output depends only on past and present inputs, so that no artificial effect can be created before the arrival of a propagating wave, for example) by an application in only one direction. However it does not conserve the phase of the signal (outphasing filter). This option should therefore not be used for processing based on phase information, e.g. array processing.
The Order of the filter defines the number of data points used for the computation of a single filtered point. Low orders less affect the signal in time but make the filter less efficient in frequency. High orders make the filter more efficient in frequency but affect more the signal in time. The default value is 2.
Cosine Taper
Cosine Taper is a linear finite impulse response (FIR) filter based on the Tukey tapering window (or tapered cosine window). This filter is definitely non-outphasing but non-causal. The Width parameter gives the width, relatively to the cut-off frequency (F1 and F2, see Figure) of the slope of the filter. Default value is 0.1 (10% of the cut-off frequency).
In the figure, the spectrum of a delta-like function (uniform spectum) as been taken as an example. The spectum is filtered with the four types of filters. The light coloured lines around the main one are located at Fi*(1-Width) and Fi*(1+Width), i being 1 (red) or 2 (blue). The specified frequencies are the limits above or below which the energy of the filtered signals is null. For instance, in the case of a band reject filter calculated between 0.5 and 3 Hz, there will absolutely no energy between 0.5 and 3 Hz.
