Geopsy: Taper - Revision history

Marc: /* Why tapering a signal? */

2011-03-30T14:57:41Z

Why tapering a signal?

Marc: /* Why tapering a signal? */

2011-03-30T14:54:43Z

Why tapering a signal?

Clotaire Michel at 13:44, 12 March 2010

2010-03-12T13:44:55Z

Pierre-Yves Bard: /* Why tapering a signal? */

2010-03-11T16:52:26Z

Why tapering a signal?

Pierre-Yves Bard: /* Options */

2010-03-11T16:51:11Z

Options

Clotaire Michel at 16:14, 10 March 2010

2010-03-10T16:14:45Z

Clotaire Michel at 16:13, 10 March 2010

2010-03-10T16:13:55Z

Clotaire Michel at 16:02, 10 March 2010

2010-03-10T16:02:40Z

Clotaire Michel at 15:57, 10 March 2010

2010-03-10T15:57:35Z

Bertrand Guillier at 15:02, 10 March 2010

2010-03-10T15:02:58Z

@@ Line 17: / Line 17: @@
 ==Why tapering a signal?==
-Since the Fourier Transform of a boxcar function (too simple tapering window, equivalent to no taper) is a [[Wikipedia:Sinc function|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 [[Wikipedia:Sinc function|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 [[Geopsy: View_menu#Fourier Transform|going to the frequency domain]]. Applying a taper for each window to compute spectra in the advanced signal processing tools is strongly recommended.
+Since the Fourier Transform of a boxcar function (too simple tapering window, equivalent to no taper) is a [[Wikipedia:Sinc function|sinc function]], the Fourier Transform of a signal without applying an appropriate [[Wikipedia:Window_function|Taper]] will be the convolution of the true Fourier Transform by the [[Wikipedia:Sinc function|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 [[Geopsy: View_menu#Fourier Transform|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==
 [[Wikipedia:Window_function|Window function (Wikipedia)]]

@@ Line 17: / Line 17: @@
 ==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 less distorts the Fourier Transform of the signal. It is therefore necessary to apply a taper before [[Geopsy: View_menu#Fourier Transform|going to the frequency domain]]. Applying a taper for each window to compute spectra in the advanced signal processing tools is strongly recommended.
+Since the Fourier Transform of a boxcar function (too simple tapering window, equivalent to no taper) is a [[Wikipedia:Sinc function|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 [[Wikipedia:Sinc function|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 [[Geopsy: View_menu#Fourier Transform|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==
 [[Wikipedia:Window_function|Window function (Wikipedia)]]

@@ Line 1: / Line 1: @@
 [[Image:Waveform-tapertime2.png|thumb|right|300px|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 [[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 some [[Geopsy: Tools|advanced signal processing tools]] on each selected window by checking the checkbox ''Use cosine taper'' in the ''Processing'' tab. The applied taper is a [[Wikipedia:Window_function#Tukey window|tapered cosine window (Tukey window)]]. When used from the [[Geopsy: Waveform Menu|Waveform menu]], ''Taper'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
+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 some [[Geopsy: Tools|advanced signal processing tools]] on each selected window by checking the checkbox ''Use cosine taper'' in the ''Processing'' tab. The applied taper is a [[Wikipedia:Window_function#Tukey window|tapered cosine window (Tukey window)]]. When used from the [[Geopsy: Waveform Menu|Waveform menu]], ''Taper'' creates new [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
 ==Options==

@@ Line 17: / Line 17: @@
 ==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#Fourier Transform|going to the frequency domain]]. Applying a taper for each window to compute spectra in the advanced signal processing tools is strongly recommended.
+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 less distorts the Fourier Transform of the signal. It is therefore necessary to apply a taper before [[Geopsy: View_menu#Fourier Transform|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==
 [[Wikipedia:Window_function|Window function (Wikipedia)]]

@@ Line 10: / Line 10: @@
 [[Image:Waveform-tapertime.png|thumb|right|300px|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 slope of the taper, as also defined for the [[Geopsy: Filter#Cosine Taper|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.
+*''Width'' allows to give the width, in % of the time interval, of each side lobe of the taper, as also defined for the [[Geopsy: Filter#Cosine Taper|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.

@@ Line 8: / Line 8: @@
 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|20% Taper function applied to a signal (top: original signal; bottom: modified signal.]]
+[[Image:Waveform-tapertime.png|thumb|right|300px|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 slope of the taper, as also defined for the [[Geopsy: Filter#Cosine Taper|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.

← Older revision		Revision as of 16:13, 10 March 2010
Line 1:		Line 1:
−	[[Image:Waveform-tapertime2.png\|thumb\|right\|300px\|Cosine taper function in time domain.]]	+	[[Image:Waveform-tapertime2.png\|thumb\|right\|300px\|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 [[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 some [[Geopsy: Tools\|advanced signal processing tools]] on each selected window by checking the checkbox ''Use cosine taper'' in the ''Processing'' tab. The applied taper is a [[Wikipedia:Window_function#Tukey window\|tapered cosine window (Tukey window)]]. When used from the [[Geopsy: Waveform Menu\|Waveform menu]], ''Taper'' modifies the [[Geopsy: Temporary Signal\|temporary signals]] in the active viewer.		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 some [[Geopsy: Tools\|advanced signal processing tools]] on each selected window by checking the checkbox ''Use cosine taper'' in the ''Processing'' tab. The applied taper is a [[Wikipedia:Window_function#Tukey window\|tapered cosine window (Tukey window)]]. When used from the [[Geopsy: Waveform Menu\|Waveform menu]], ''Taper'' modifies the [[Geopsy: Temporary Signal\|temporary signals]] in the active viewer.

← Older revision		Revision as of 15:02, 10 March 2010
Line 1:		Line 1:
−	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.	+	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==		==Options==