HRFK - Revision history

Pierre-Yves Bard: /* Parameter settings */

2010-03-11T09:08:16Z

Parameter settings

2010-03-10T14:34:41Z

Parameter settings

2010-03-10T14:26:17Z

Parameter settings

2010-03-10T13:38:12Z

High resolution frequency wavenumber Toolbox (Capon's method) - overview

2010-03-10T13:25:22Z

High resolution frequency wavenumber Toolbox (Capon's method) - overview

2010-03-09T17:52:26Z

Contents of output file

2010-03-09T17:51:35Z

2010-03-09T17:50:37Z

Graphical display of high resolution f-k results using max2curve

2010-03-09T17:49:20Z

@@ Line 39: / Line 39: @@
 The stabilization can be achieved by [[Wikipedia:Diagonal_Loading|diagonal loading]], sometimes
-also referred to by damping using a regularization parameter. The '''damping factor''' ist the new optional parameter in the
+also referred to by damping using a regularization parameter. The '''damping factor''' is the new optional parameter in the
 high-resolution frequency wavenumber toolbox. A good value is usually found by trial and error, but a good starting value is probably
 .001 to 0.01.

@@ Line 35: / Line 35: @@
 Compared to the conventional f-k toolbox, there is just one single (optional!) parameter that is included in the ''processing
 tab'' of the toolbox. As the calculation for the hrfk algorithm involves the inversion of
-the cross spectral matrix estimate from the data ([[see above]]), it may sometimes be necessary to stabilize the
+the cross spectral matrix estimate from the data ([[HRFK#High_resolution_frequency_wavenumber_Toolbox_.28Capon.27s_method.29_-_overview|see above]]), it may sometimes be necessary to stabilize the
 cross spectral matrix before inverting.

@@ Line 10: / Line 10: @@
 <math>
-BP_{Capon}(\omega,\vec{k}) = \frac{1}{\vec{e}^\dagger(\omega,\vec{k})\underline{R}^{-1}(\omega)\vec{e}(\omega,\vec{k})
+BP_{Capon}(\omega,\vec{k}) = \frac{1}{\vec{e}^\dagger(\omega,\vec{k})\underline{R}^{-1}(\omega)\vec{e}(\omega,\vec{k})}
 </math>
 where <math>\underline{R}^{-1}(\omega)</math> is simply the inverse of the cross spectral matrix estimate and <math>\vec{e}</math>
 is the so-called steering vector summarizing the shift times for the harmonic plane wave with wavenumber vector <math>\vec{k}</math>
-for each station within the array.
+for each station within the array.The <math>\dagger</math> symbol presents the conjugate transpose operation. In the same notation,
-The corresponding toolbox that can be called using the following
+For further details, we refer you to the [[Array_signal_processing|array signal processing]] page of this wiki. Here we only
-plugin icon [[Image:HRFKPluginIcon.png|32px]] can be used straightforward in nearly the same way
+emphasize, that the inverse of the cross-spectral matrix has to be computed for the high-resolution technique, making the
-as the conventional f-k toolbox.
+estimate potentially unstable.
 == Parameter settings ==

@@ Line 32: / Line 32: @@
 == Parameter settings ==
-There is just one more (optional!) parameter that can be set. The calcuation for the hrfk algorithm involves the inversion of
+[[Image:HRFKToolboxProcessingTab.png|thumb|left|350px|High resolution frequency wavenumber toolbox - processing tab]]
-the cross spectral matrix estimate from the data. In order to guarantee a numerically stable solution for the Matrix inversion,
+Compared to the conventional f-k toolbox, there is just one single (optional!) parameter that is included in the ''processing
-a regularization parameter (damping constant) can be provided to load the diagonal of the cross spectral matrix before inversion.
+tab'' of the toolbox. As the calculation for the hrfk algorithm involves the inversion of
-Note: by doing so (using a damping constant), you will smooth out your wavenumber power spectra and eventually not obtain
+The stabilization can be achieved by [[Wikipedia:Diagonal_Loading|diagonal loading]], sometimes
-much better results compared to the conventional beamforming approach.
+also referred to by damping using a regularization parameter. The '''damping factor''' ist the new optional parameter in the
 == Contents of output file ==

@@ Line 2: / Line 2: @@
 The high resolution frequency wavenumber (hrfk) algorithm follows the ideas of Capon (1969)
-<ref name="Capon (1969)"> Capon, 1969. xxx ,IEEE Proceedings, , , .</ref>
+<ref name="Capon (1969)"> Capon, J., High-Resolution Frequency-Wavenumber Spectrum Analysis, Proceedings of the IEEE, 57, No. 8, 1408-1419, 1969.</ref>.
-. The corresponding toolbox that can be called using the following
+The Capon beamformer relies on a very simple formula:
 plugin icon [[Image:HRFKPluginIcon.png|32px]] can be used straightforward in nearly the same way
 as the conventional f-k toolbox.

@@ Line 20: / Line 20: @@
 The output files for the high resolution f-k approach are equivalent and compatible to the output
-files produced with the conventional approach. For details check [[FK: output files|the following page]].
+files produced with the conventional approach. For details check [[FK#Contents_of_output_file|the following page]].
 == Graphical display of high resolution f-k results using max2curve ==

@@ Line 25: / Line 25: @@
 The usage of [[max2curve]] is equivalent to using this tool with .max files produced
-with the conventional f-k approach. Check also [[FK#Result|the following page]] for details.
+with the conventional f-k approach. Check also [[FK#Graphical_display_of_f-k_results_using_max2curve|the following page]] for details.
 == References ==
 <references/>