Difference between revisions of "Geopsy: Taper"
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| − | 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 [[Geopsy: Waveform Menu|Waveform menu]], that applies a tapering function to the signals in the active [[Geopsy: Signal Viewer|signal viewer]]. It can also be used in the [[Geopsy: Tools|advanced signal processing tools]] on each selected window. The applied taper is a tapered cosine window [[Wikipedia:Window_function#Tukey window|(Tukey window)]]. | + | 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 [[Geopsy: Waveform Menu|Waveform menu]], that applies a tapering function to the signals in the active [[Geopsy: Signal Viewer|signal viewer]]. It can also be used in the [[Geopsy: Tools|advanced signal processing tools]] [[Geopsy: Spectrum|Spectrum]], [[Geopsy: Spectrum rotate|Spectrum rotate]], [[Geopsy: H/V|H/V]], [[Geopsy: H/V rotate|H/V rotate]] on each selected window by checking the checkbox ''Use cosine taper'' in the ''Processing'' tab. The applied taper is a tapered cosine window [[Wikipedia:Window_function#Tukey window|(Tukey window)]]. When used from the [[Geopsy: Waveform Menu|Waveform menu]], ''Taper'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer. |
| − | + | ==Options== | |
| + | By clicking on ''Taper'', a pop-up window appears with the following options: | ||
*[[Geopsy: Time Limits|''Time Limits'']] allows to specify the time interval out of which the signal will be set to 0. | *[[Geopsy: Time Limits|''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 [[Geopsy: Waveform Menu|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...). | ||
| − | + | [[Image:Waveform-tapertime.png|thumb|right|300px|Cosine taper function in time domain.]] | |
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| − | + | *''Width'' allows to give the width, in % of the time interval, of the slopes of the taper as also defined for the [[Geopsy: Filter#Cosine Taper|cosine taper filter]] but in the frequency domain. Half of the width is affected to the up-going slope, the other half to the down-going slope. | |
| − | + | When used from an advanced processing tool, only this last parameter can be set. | |
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| − | Note: | + | Note: When used from the [[Geopsy: Waveform Menu|Waveform menu]], the signal is set to 0 out of the taper function, but not cut. To cut the signal, use the [[Geopsy: Cut|corresponding option]]. |
==Why tapering a signal?== | ==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 [[Wikipedia:Window_function|Taper]] will be the multiplication of the true Fourier Transform by the sinc function. On the contrary, appropriate tapers have a Fourier Transform closer to a Dirac function that distorts less the Fourier Transform of the signal. It is therefore necessary to apply a taper before [[Geopsy: View_Menu#Frequency (amplitude)|going to the frequency domain]]. | + | 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 [[Wikipedia:Window_function|Taper]] will be the multiplication of the true Fourier Transform by the sinc function. On the contrary, appropriate tapers have a Fourier Transform closer to a Dirac function that distorts less the Fourier Transform of the signal. It is therefore necessary to apply a taper before [[Geopsy: View_Menu#Frequency (amplitude)|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== | ==See also== | ||
[[Wikipedia:Window_function|Window function (Wikipedia)]] | [[Wikipedia:Window_function|Window function (Wikipedia)]] | ||
Revision as of 08:43, 10 March 2010
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 the advanced signal processing tools Spectrum, Spectrum rotate, H/V, H/V rotate 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 modifies the 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...).
- Width allows to give the width, in % of the time interval, of the slopes of the taper as also defined for the cosine taper filter but in the frequency domain. Half of the width is affected to the up-going slope, the other half to the down-going slope.
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 multiplication of the true Fourier Transform by the sinc function. On the contrary, appropriate tapers have a Fourier Transform closer to a Dirac function that distorts less 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.
