Geopsy: Wavelet transform - Revision history

Clotaire Michel at 13:46, 12 March 2010

2010-03-12T13:46:23Z

Pierre-Yves Bard at 09:10, 12 March 2010

2010-03-12T09:10:58Z

Pierre-Yves Bard at 09:00, 12 March 2010

2010-03-12T09:00:57Z

Pierre-Yves Bard at 08:53, 12 March 2010

2010-03-12T08:53:36Z

Pierre-Yves Bard at 08:27, 12 March 2010

2010-03-12T08:27:45Z

Clotaire Michel at 17:03, 10 March 2010

2010-03-10T17:03:32Z

Clotaire Michel at 14:06, 10 March 2010

2010-03-10T14:06:53Z

Clotaire Michel: New page: '''Wavelet transform''', reached from the Waveform menu, performs the Wavelet Transform of the signals in the active [[Geopsy: Sig...

2010-03-10T13:00:19Z

New page: '''Wavelet transform''', reached from the Waveform menu, performs the Wavelet Transform of the signals in the active [[Geopsy: Sig...

New page

'''Wavelet transform''', reached from the [[Geopsy: Waveform Menu|Waveform menu]], performs the [[Wikipedia:Wavelet Transform|Wavelet Transform]] of the signals in the active [[Geopsy: Signal Viewer|signal viewer]].
By clicking on ''Wavelet transform'', a pop-up window appears asking for the following option:
*''m'' is the parameter of the wavelet
*''fi'' is the wavelet central frequency in Hertz

The pop-up window also displays the values ''DT'' and ''DF''

This tool applies a [[Wikipedia:Morlet Wavelet|Morlet wavelet]] of central frequency ''fi'' with the provided ''m'' parameter to the

"Wavelet transform" modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.

@@ Line 2: / Line 2: @@
 In [[Geopsy]], a [[Wikipedia:Wavelet_series#Wavelet transform|'''Wavelet transform''']] can be either applied at a single frequency using the [[Geopsy: Waveform Menu|Waveform menu]] or on a broad frequency range using the [[Geopsy: Time Frequency Analysis|Time Frequency Analysis toolbox]].
-When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
+When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' creates new [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
 The parameters requested for the Wavelet transform are:
 *''m'', the parameter of the wavelet. It characterizes the trade-off between time and frequency resolutions. The default value for ''m'' is 10. Increasing m leads to better frequency resolution, but lower time resolution.

← Older revision		Revision as of 09:10, 12 March 2010
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−	Applying a Wavelet transform at a given frequency ''fi'' allows to analyze in time ~~the~~ energy of the signal at that frequency. ~~Moreover, the~~ [[Geopsy: Time Frequency Analysis\|TFA toolbox]] applies the Wavelet transform at each frequency to provide a time-frequency plot that distributes the energy of the signal in the time-frequency plane.	+	Applying a Wavelet transform at a given frequency ''fi'' allows to analyze the time distribution of energy of the signal at that particular frequency.
		+	The [[Geopsy: Time Frequency Analysis\|TFA toolbox]] applies the Wavelet transform at each frequency to provide a time-frequency plot that distributes the energy of the signal in the time-frequency plane.

	See also:		See also:

@@ Line 4: / Line 4: @@
 When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
 The parameters requested for the Wavelet transform are:
-*''m'', the parameter of the wavelet. It characterizes the trade-off between time and frequency resolutions. The default value for ''m'' is 10.
+*''m'', the parameter of the wavelet. It characterizes the trade-off between time and frequency resolutions. The default value for ''m'' is 10. Increasing m leads to better frequency resolution, but lower time resolution.
 *''fi'' , the wavelet central frequency in Hertz, i.e. the analyzed frequency. This parameter is not used in the [[Geopsy: Time Frequency Analysis|TFA toolbox]].
@@ Line 11: / Line 11: @@
 The Wavelet transform multiplies in the frequency domain the signals with a [[Wikipedia:Morlet_wavelet|Modified Morlet wavelet]] of central frequency ''fi'' and parameter ''m'' to the signal:
-<math>M(f)=\frac{1}{\pi^{\frac{1}{4}}}e^{w_0^2(\frac{f}{fi}-1)^2m}</math>, with <math>w_0=6</math>.
+<math>M(f)=\frac{1}{\pi^{\frac{1}{4}}}e^{-w_0^2(\frac{f}{fi}-1)^2m}</math>, with <math>w_0=6</math>.

@@ Line 4: / Line 4: @@
 When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
 The parameters requested for the Wavelet transform are:
-*''m'', the parameter of the wavelet. It allows trade between time and frequency resolutions. The default value for ''m'' is 10.
+*''m'', the parameter of the wavelet. It characterizes the trade-off between time and frequency resolutions. The default value for ''m'' is 10.
 *''fi'' , the wavelet central frequency in Hertz, i.e. the analyzed frequency. This parameter is not used in the [[Geopsy: Time Frequency Analysis|TFA toolbox]].

@@ Line 2: / Line 2: @@
 In [[Geopsy]], a [[Wikipedia:Wavelet_series#Wavelet transform|'''Wavelet transform''']] can be either applied at a single frequency using the [[Geopsy: Waveform Menu|Waveform menu]] or on a broad frequency range using the [[Geopsy: Time Frequency Analysis|Time Frequency Analysis toolbox]].
-When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer..
+When reached through the [[Geopsy: Waveform Menu|Waveform menu]] ''Wavelet transform'' modifies the [[Geopsy: Temporary Signal|temporary signals]] in the active viewer.
 The parameters requested for the Wavelet transform are:
 *''m'', the parameter of the wavelet. It allows trade between time and frequency resolutions. The default value for ''m'' is 10.

@@ Line 1: / Line 1: @@
 In [[Geopsy]], a [[Wikipedia:Wavelet_series#Wavelet transform|'''Wavelet transform''']] can be either applied at a single frequency using the [[Geopsy: Waveform Menu|Waveform menu]] or on a broad frequency range using the [[Geopsy: Time Frequency Analysis|Time Frequency Analysis toolbox]].
@@ Line 5: / Line 6: @@
 *''m'', the parameter of the wavelet. It allows trade between time and frequency resolutions. The default value for ''m'' is 10.
 *''fi'' , the wavelet central frequency in Hertz, i.e. the analyzed frequency. This parameter is not used in the [[Geopsy: Time Frequency Analysis|TFA toolbox]].
 The wavelet box also displays the time resolution ''DT'' (in seconds) and the frequency resolution ''DF'' (in Hertz) of the Wavelet. In the [[Geopsy: Time Frequency Analysis|TFA toolbox]], providing the analyzed frequency only allows to compute these time and frequency resolutions for various frequency before the computing starts.
 The Wavelet transform multiplies in the frequency domain the signals with a [[Wikipedia:Morlet_wavelet|Modified Morlet wavelet]] of central frequency ''fi'' and parameter ''m'' to the signal:
 <math>M(f)=\frac{1}{\pi^{\frac{1}{4}}}e^{w_0^2(\frac{f}{fi}-1)^2m}</math>, with <math>w_0=6</math>.
 Applying a Wavelet transform at a given frequency ''fi'' allows to analyze in time the energy of the signal at that frequency. Moreover, the [[Geopsy: Time Frequency Analysis|TFA toolbox]] applies the Wavelet transform at each frequency to provide a time-frequency plot that distributes the energy of the signal in the time-frequency plane.
@@ Line 15: / Line 19: @@
 *[[Wikipedia:Wavelet_series#Wavelet transform|Wavelet Transform (Wikipedia)]]
 *[[Wikipedia:Morlet_wavelet|Morlet wavelet (Wikipedia)]]