Geopsy: Taper

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Cosine taper function of 20% width in time domain.

A Taper (or apodization function or window function) is applied to a time signal to improve its properties in the frequency domain. Taper is a tool reached from the Waveform menu, that applies a tapering function to the signals in the active signal viewer. It can also be used in some advanced signal processing tools on each selected window by checking the checkbox Use cosine taper in the Processing tab. The applied taper is a tapered cosine window (Tukey window). When used from the Waveform menu, Taper creates new temporary signals in the active viewer.

Options

By clicking on Taper, a pop-up window appears with the following options:

  • Time Limits allows to specify the time interval out of which the signal will be set to 0.

The checkbox Use only the properties of the first signal, available when used from the Waveform menu, forces to use the same tapering function for all signals (the one computed for the first signal), whatever the properties of the other signals (starting time, length...).

20% Taper function applied to a signal (top: original signal; bottom: modified signal.)
  • Width allows to give the width, in % of the time interval, of each side lobe of the taper, as also defined for the cosine taper filter but in the frequency domain. Width is applied both to the up-going and down-going slope so that 50% is a maximum value, corresponding to a pure cosine function.

When used from an advanced processing tool, only this last parameter can be set.

Note: When used from the Waveform menu, the signal is set to 0 out of the taper function, but not cut. To cut the signal, use the corresponding option.

Why tapering a signal?

Since the Fourier Transform of a boxcar function (too simple tapering window, equivalent to no taper) is a sinc function, the Fourier Transform of a signal without applying an appropriate Taper will be the convolution of the true Fourier Transform by the sinc function. On the contrary, appropriate tapers have a Fourier Transform closer to a Dirac function that less distorts the Fourier Transform of the signal. It is therefore necessary to apply a taper before going to the frequency domain. Applying a taper for each window to compute spectra in the advanced signal processing tools is strongly recommended.

See also

Window function (Wikipedia)