tdehaeze/dehaeze19_compl_filter_shapin_using_synth
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Add all code as Zip file

Browse Source
This commit is contained in:
Thomas Dehaeze 2020-07-16 14:59:27 +02:00
parent 7e54314794
commit 10aa52cba1
3 changed files with 94 additions and 83 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

167
matlab/index.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-07-16 jeu. 14:54 -->
<!-- 2020-07-16 jeu. 14:59 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Matlab Computation</title>
<meta name="generator" content="Org mode" />
@ -34,29 +34,29 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org46404f2">1. H-Infinity synthesis of complementary filters</a>
<li><a href="#org572bfb6">1. H-Infinity synthesis of complementary filters</a>
<ul>
<li><a href="#org806b4f7">1.1. Synthesis Architecture</a></li>
<li><a href="#orgabe6aad">1.2. Design of Weighting Function</a></li>
<li><a href="#org2aaba6e">1.3. H-Infinity Synthesis</a></li>
<li><a href="#orgcb4ac14">1.4. Obtained Complementary Filters</a></li>
<li><a href="#org82eca6b">1.1. Synthesis Architecture</a></li>
<li><a href="#org0030590">1.2. Design of Weighting Function</a></li>
<li><a href="#org4aa1049">1.3. H-Infinity Synthesis</a></li>
<li><a href="#org9c89267">1.4. Obtained Complementary Filters</a></li>
</ul>
</li>
<li><a href="#org2feffce">2. Generating 3 complementary filters</a>
<li><a href="#org2da98fb">2. Generating 3 complementary filters</a>
<ul>
<li><a href="#orgb8aee19">2.1. Theory</a></li>
<li><a href="#org6e5d31d">2.2. Weights</a></li>
<li><a href="#org9a698ee">2.3. H-Infinity Synthesis</a></li>
<li><a href="#orgf23da1c">2.4. Obtained Complementary Filters</a></li>
<li><a href="#org0abd7a4">2.1. Theory</a></li>
<li><a href="#org752b7ef">2.2. Weights</a></li>
<li><a href="#org28adeaa">2.3. H-Infinity Synthesis</a></li>
<li><a href="#org1366f58">2.4. Obtained Complementary Filters</a></li>
</ul>
</li>
<li><a href="#org0f85e92">3. Try to implement complementary filters for LIGO</a>
<li><a href="#org4f214f0">3. Try to implement complementary filters for LIGO</a>
<ul>
<li><a href="#orgb61077c">3.1. Specifications</a></li>
<li><a href="#orgbc85105">3.2. FIR Filter</a></li>
<li><a href="#org7637994">3.3. Weights</a></li>
<li><a href="#org173e2c3">3.4. H-Infinity Synthesis</a></li>
<li><a href="#org0e40b72">3.5. Compare FIR and H-Infinity Filters</a></li>
<li><a href="#orga7890e4">3.1. Specifications</a></li>
<li><a href="#org3e8a45e">3.2. FIR Filter</a></li>
<li><a href="#orgb67b5e5">3.3. Weights</a></li>
<li><a href="#org7521851">3.4. H-Infinity Synthesis</a></li>
<li><a href="#org8f5b230">3.5. Compare FIR and H-Infinity Filters</a></li>
</ul>
</li>
</ul>
@ -78,16 +78,23 @@ To achieve this, the sensors included in the filter should complement one anothe
</blockquote>
<ul class="org-ul">
<li>in section <a href="#org48961a2">1</a>, the \(\mathcal{H}_\infty\) synthesis is used for generating two complementary filters (<a href="matlab/h_inf_synthesis_complementary_filters.m">matlab code</a>)</li>
<li>in section <a href="#org37eeb9f">2</a>, a method using the \(\mathcal{H}_\infty\) synthesis is proposed to shape three of more complementary filters (<a href="matlab/three_comp_filters.m">matlab code</a>)</li>
<li>in section <a href="#orge05d224">3</a>, the \(\mathcal{H}_\infty\) synthesis is used and compared with FIR complementary filters used for LIGO (<a href="matlab/comp_filters_ligo.m">matlab code</a>)</li>
<li>in section <a href="#orgee3ddb1">1</a>, the \(\mathcal{H}_\infty\) synthesis is used for generating two complementary filters</li>
<li>in section <a href="#orgaa807e4">2</a>, a method using the \(\mathcal{H}_\infty\) synthesis is proposed to shape three of more complementary filters</li>
<li>in section <a href="#org9d61b55">3</a>, the \(\mathcal{H}_\infty\) synthesis is used and compared with FIR complementary filters used for LIGO</li>
</ul>
<div id="outline-container-org46404f2" class="outline-2">
<h2 id="org46404f2"><span class="section-number-2">1</span> H-Infinity synthesis of complementary filters</h2>
<div class="note">
<p>
Add the Matlab code use to obtain the results presented in the paper are accessible <a href="matlab.zip">here</a> and presented below.
</p>
</div>
<div id="outline-container-org572bfb6" class="outline-2">
<h2 id="org572bfb6"><span class="section-number-2">1</span> H-Infinity synthesis of complementary filters</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org48961a2"></a>
<a id="orgee3ddb1"></a>
</p>
<div class="note">
<p>
@ -97,8 +104,8 @@ The Matlab file corresponding to this section is accessible <a href="matlab/h_in
</div>
</div>
<div id="outline-container-org806b4f7" class="outline-3">
<h3 id="org806b4f7"><span class="section-number-3">1.1</span> Synthesis Architecture</h3>
<div id="outline-container-org82eca6b" class="outline-3">
<h3 id="org82eca6b"><span class="section-number-3">1.1</span> Synthesis Architecture</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We here synthesize two complementary filters using the \(\mathcal{H}_\infty\) synthesis.
@ -106,18 +113,18 @@ The goal is to specify upper bounds on the norms of the two complementary filter
</p>
<p>
In order to do so, we use the generalized plant shown on figure <a href="#org4993735">1</a> where \(W_1(s)\) and \(W_2(s)\) are weighting transfer functions that will be used to shape \(H_1(s)\) and \(H_2(s)\) respectively.
In order to do so, we use the generalized plant shown on figure <a href="#orge288ab9">1</a> where \(W_1(s)\) and \(W_2(s)\) are weighting transfer functions that will be used to shape \(H_1(s)\) and \(H_2(s)\) respectively.
</p>
<div id="org4993735" class="figure">
<div id="orge288ab9" class="figure">
<p><img src="figs-tikz/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
</p>
<p><span class="figure-number">Figure 1: </span>\(\mathcal{H}_\infty\) synthesis of the complementary filters</p>
</div>
<p>
The \(\mathcal{H}_\infty\) synthesis applied on this generalized plant will give a transfer function \(H_2\) (figure <a href="#org4993735">1</a>) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_1,\ z_2]\) is less than one:
The \(\mathcal{H}_\infty\) synthesis applied on this generalized plant will give a transfer function \(H_2\) (figure <a href="#orge288ab9">1</a>) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_1,\ z_2]\) is less than one:
\[ \left\| \begin{array}{c} (1 - H_2(s)) W_1(s) \\ H_2(s) W_2(s) \end{array} \right\|_\infty < 1 \]
</p>
@ -137,8 +144,8 @@ We then see that \(W_1(s)\) and \(W_2(s)\) can be used to shape both \(H_1(s)\)
</div>
</div>
<div id="outline-container-orgabe6aad" class="outline-3">
<h3 id="orgabe6aad"><span class="section-number-3">1.2</span> Design of Weighting Function</h3>
<div id="outline-container-org0030590" class="outline-3">
<h3 id="org0030590"><span class="section-number-3">1.2</span> Design of Weighting Function</h3>
<div class="outline-text-3" id="text-1-2">
<p>
A formula is proposed to help the design of the weighting functions:
@ -162,11 +169,11 @@ The parameters permits to specify:
</ul>
<p>
The general shape of a weighting function generated using the formula is shown in figure <a href="#orge551da2">2</a>.
The general shape of a weighting function generated using the formula is shown in figure <a href="#org652b9ee">2</a>.
</p>
<div id="orge551da2" class="figure">
<div id="org652b9ee" class="figure">
<p><img src="figs-tikz/weight_formula.png" alt="weight_formula.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Amplitude of the proposed formula for the weighting functions</p>
@ -182,7 +189,7 @@ W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G
</div>
<div id="org8791cc6" class="figure">
<div id="orge154b03" class="figure">
<p><img src="figs/weights_W1_W2.png" alt="weights_W1_W2.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Weights on the complementary filters \(W_1\) and \(W_2\) and the associated performance weights (<a href="./figs/weights_W1_W2.png">png</a>, <a href="./figs/weights_W1_W2.pdf">pdf</a>)</p>
@ -190,8 +197,8 @@ W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G
</div>
</div>
<div id="outline-container-org2aaba6e" class="outline-3">
<h3 id="org2aaba6e"><span class="section-number-3">1.3</span> H-Infinity Synthesis</h3>
<div id="outline-container-org4aa1049" class="outline-3">
<h3 id="org4aa1049"><span class="section-number-3">1.3</span> H-Infinity Synthesis</h3>
<div class="outline-text-3" id="text-1-3">
<p>
We define the generalized plant \(P\) on matlab.
@ -245,7 +252,7 @@ Test bounds: 0.1000 &lt; gamma &lt;= 1050.0000
</pre>
<p>
We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H_1\) and \(H_2\) is shown on figure <a href="#org4f60b38">4</a>.
We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H_1\) and \(H_2\) is shown on figure <a href="#org0a27d96">4</a>.
</p>
<div class="org-src-container">
@ -255,15 +262,15 @@ We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H
</div>
</div>
<div id="outline-container-orgcb4ac14" class="outline-3">
<h3 id="orgcb4ac14"><span class="section-number-3">1.4</span> Obtained Complementary Filters</h3>
<div id="outline-container-org9c89267" class="outline-3">
<h3 id="org9c89267"><span class="section-number-3">1.4</span> Obtained Complementary Filters</h3>
<div class="outline-text-3" id="text-1-4">
<p>
The obtained complementary filters are shown on figure <a href="#org4f60b38">4</a>.
The obtained complementary filters are shown on figure <a href="#org0a27d96">4</a>.
</p>
<div id="org4f60b38" class="figure">
<div id="org0a27d96" class="figure">
<p><img src="figs/hinf_filters_results.png" alt="hinf_filters_results.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Obtained complementary filters using \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_filters_results.png">png</a>, <a href="./figs/hinf_filters_results.pdf">pdf</a>)</p>
@ -272,11 +279,11 @@ The obtained complementary filters are shown on figure <a href="#org4f60b38">4</
</div>
</div>
<div id="outline-container-org2feffce" class="outline-2">
<h2 id="org2feffce"><span class="section-number-2">2</span> Generating 3 complementary filters</h2>
<div id="outline-container-org2da98fb" class="outline-2">
<h2 id="org2da98fb"><span class="section-number-2">2</span> Generating 3 complementary filters</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org37eeb9f"></a>
<a id="orgaa807e4"></a>
</p>
<div class="note">
<p>
@ -286,8 +293,8 @@ The Matlab file corresponding to this section is accessible <a href="matlab/thre
</div>
</div>
<div id="outline-container-orgb8aee19" class="outline-3">
<h3 id="orgb8aee19"><span class="section-number-3">2.1</span> Theory</h3>
<div id="outline-container-org0abd7a4" class="outline-3">
<h3 id="org0abd7a4"><span class="section-number-3">2.1</span> Theory</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We want:
@ -300,11 +307,11 @@ We want:
\end{align*}
<p>
For that, we use the \(\mathcal{H}_\infty\) synthesis with the architecture shown on figure <a href="#orgd8125a2">5</a>.
For that, we use the \(\mathcal{H}_\infty\) synthesis with the architecture shown on figure <a href="#orgf60646a">5</a>.
</p>
<div id="orgd8125a2" class="figure">
<div id="orgf60646a" class="figure">
<p><img src="figs-tikz/comp_filter_three_hinf.png" alt="comp_filter_three_hinf.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Generalized architecture for generating 3 complementary filters</p>
@ -325,8 +332,8 @@ And thus if we choose \(H_1 = 1 - H_2 - H_3\) we have solved the problem.
</div>
</div>
<div id="outline-container-org6e5d31d" class="outline-3">
<h3 id="org6e5d31d"><span class="section-number-3">2.2</span> Weights</h3>
<div id="outline-container-org752b7ef" class="outline-3">
<h3 id="org752b7ef"><span class="section-number-3">2.2</span> Weights</h3>
<div class="outline-text-3" id="text-2-2">
<p>
First we define the weights.
@ -343,7 +350,7 @@ W3 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G
</div>
<div id="orgfaded1f" class="figure">
<div id="orgbe161b9" class="figure">
<p><img src="figs/three_weighting_functions.png" alt="three_weighting_functions.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Three weighting functions used for the \(\mathcal{H}_\infty\) synthesis of the complementary filters (<a href="./figs/three_weighting_functions.png">png</a>, <a href="./figs/three_weighting_functions.pdf">pdf</a>)</p>
@ -351,8 +358,8 @@ W3 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G
</div>
</div>
<div id="outline-container-org9a698ee" class="outline-3">
<h3 id="org9a698ee"><span class="section-number-3">2.3</span> H-Infinity Synthesis</h3>
<div id="outline-container-org28adeaa" class="outline-3">
<h3 id="org28adeaa"><span class="section-number-3">2.3</span> H-Infinity Synthesis</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Then we create the generalized plant <code>P</code>.
@ -408,8 +415,8 @@ Test bounds: 0.1000 &lt; gamma &lt;= 1050.0000
</div>
</div>
<div id="outline-container-orgf23da1c" class="outline-3">
<h3 id="orgf23da1c"><span class="section-number-3">2.4</span> Obtained Complementary Filters</h3>
<div id="outline-container-org1366f58" class="outline-3">
<h3 id="org1366f58"><span class="section-number-3">2.4</span> Obtained Complementary Filters</h3>
<div class="outline-text-3" id="text-2-4">
<p>
The obtained filters are:
@ -422,7 +429,7 @@ H1 = 1 - H2 - H3;
</div>
<div id="org2bb2f66" class="figure">
<div id="org4580cd5" class="figure">
<p><img src="figs/three_complementary_filters_results.png" alt="three_complementary_filters_results.png" />
</p>
<p><span class="figure-number">Figure 7: </span>The three complementary filters obtained after \(\mathcal{H}_\infty\) synthesis (<a href="./figs/three_complementary_filters_results.png">png</a>, <a href="./figs/three_complementary_filters_results.pdf">pdf</a>)</p>
@ -431,11 +438,11 @@ H1 = 1 - H2 - H3;
</div>
</div>
<div id="outline-container-org0f85e92" class="outline-2">
<h2 id="org0f85e92"><span class="section-number-2">3</span> Try to implement complementary filters for LIGO</h2>
<div id="outline-container-org4f214f0" class="outline-2">
<h2 id="org4f214f0"><span class="section-number-2">3</span> Try to implement complementary filters for LIGO</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orge05d224"></a>
<a id="org9d61b55"></a>
</p>
<div class="note">
<p>
@ -453,8 +460,8 @@ The FIR complementary filters designed in (<a href="#citeproc_bib_item_1">Hua 20
</p>
</div>
<div id="outline-container-orgb61077c" class="outline-3">
<h3 id="orgb61077c"><span class="section-number-3">3.1</span> Specifications</h3>
<div id="outline-container-orga7890e4" class="outline-3">
<h3 id="orga7890e4"><span class="section-number-3">3.1</span> Specifications</h3>
<div class="outline-text-3" id="text-3-1">
<p>
The specifications for the filters are:
@ -467,11 +474,11 @@ The specifications for the filters are:
</ol>
<p>
The specifications are translated in upper bounds of the complementary filters are shown on figure <a href="#org480bed5">8</a>.
The specifications are translated in upper bounds of the complementary filters are shown on figure <a href="#org66a1abf">8</a>.
</p>
<div id="org480bed5" class="figure">
<div id="org66a1abf" class="figure">
<p><img src="figs/ligo_specifications.png" alt="ligo_specifications.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Specification for the LIGO complementary filters (<a href="./figs/ligo_specificationss.png">png</a>, <a href="./figs/ligo_specificationss.pdf">pdf</a>)</p>
@ -479,8 +486,8 @@ The specifications are translated in upper bounds of the complementary filters a
</div>
</div>
<div id="outline-container-orgbc85105" class="outline-3">
<h3 id="orgbc85105"><span class="section-number-3">3.2</span> FIR Filter</h3>
<div id="outline-container-org3e8a45e" class="outline-3">
<h3 id="org3e8a45e"><span class="section-number-3">3.2</span> FIR Filter</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We here try to implement the FIR complementary filter synthesis as explained in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
@ -638,7 +645,7 @@ h = y(2:end);
</pre>
<p>
Finally, we compute the filter response over the frequency vector defined and the result is shown on figure <a href="#org94db411">9</a> which is very close to the filters obtain in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
Finally, we compute the filter response over the frequency vector defined and the result is shown on figure <a href="#org2bf8c02">9</a> which is very close to the filters obtain in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
</p>
<div class="org-src-container">
@ -648,7 +655,7 @@ H = [exp(-j*kron(w'.*2*pi,[0:n-1]))]*h;
</div>
<div id="org94db411" class="figure">
<div id="org2bf8c02" class="figure">
<p><img src="figs/fir_filter_ligo.png" alt="fir_filter_ligo.png" />
</p>
<p><span class="figure-number">Figure 9: </span>FIR Complementary filters obtain after convex optimization (<a href="./figs/fir_filter_ligo.png">png</a>, <a href="./figs/fir_filter_ligo.pdf">pdf</a>)</p>
@ -656,8 +663,8 @@ H = [exp(-j*kron(w'.*2*pi,[0:n-1]))]*h;
</div>
</div>
<div id="outline-container-org7637994" class="outline-3">
<h3 id="org7637994"><span class="section-number-3">3.3</span> Weights</h3>
<div id="outline-container-orgb67b5e5" class="outline-3">
<h3 id="orgb67b5e5"><span class="section-number-3">3.3</span> Weights</h3>
<div class="outline-text-3" id="text-3-3">
<p>
We design weights that will be used for the \(\mathcal{H}_\infty\) synthesis of the complementary filters.
@ -671,11 +678,11 @@ Here are the requirements on the filters:
</ul>
<p>
The bode plot of the weights is shown on figure <a href="#org05a38e8">10</a>.
The bode plot of the weights is shown on figure <a href="#orgbfc5afc">10</a>.
</p>
<div id="org05a38e8" class="figure">
<div id="orgbfc5afc" class="figure">
<p><img src="figs/ligo_weights.png" alt="ligo_weights.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Weights for the \(\mathcal{H}_\infty\) synthesis (<a href="./figs/ligo_weights.png">png</a>, <a href="./figs/ligo_weights.pdf">pdf</a>)</p>
@ -683,11 +690,11 @@ The bode plot of the weights is shown on figure <a href="#org05a38e8">10</a>.
</div>
</div>
<div id="outline-container-org173e2c3" class="outline-3">
<h3 id="org173e2c3"><span class="section-number-3">3.4</span> H-Infinity Synthesis</h3>
<div id="outline-container-org7521851" class="outline-3">
<h3 id="org7521851"><span class="section-number-3">3.4</span> H-Infinity Synthesis</h3>
<div class="outline-text-3" id="text-3-4">
<p>
We define the generalized plant as shown on figure <a href="#org4993735">1</a>.
We define the generalized plant as shown on figure <a href="#orge288ab9">1</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">P = [0 wL;
@ -746,11 +753,11 @@ State-space model with 1 outputs, 1 inputs, and 27 states.
</pre>
<p>
The bode plot of the obtained filters as shown on figure <a href="#orgc5e003d">11</a>.
The bode plot of the obtained filters as shown on figure <a href="#org0f497c3">11</a>.
</p>
<div id="orgc5e003d" class="figure">
<div id="org0f497c3" class="figure">
<p><img src="figs/hinf_synthesis_ligo_results.png" alt="hinf_synthesis_ligo_results.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Obtained complementary filters using the \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_synthesis_ligo_results.png">png</a>, <a href="./figs/hinf_synthesis_ligo_results.pdf">pdf</a>)</p>
@ -758,15 +765,15 @@ The bode plot of the obtained filters as shown on figure <a href="#orgc5e003d">1
</div>
</div>
<div id="outline-container-org0e40b72" class="outline-3">
<h3 id="org0e40b72"><span class="section-number-3">3.5</span> Compare FIR and H-Infinity Filters</h3>
<div id="outline-container-org8f5b230" class="outline-3">
<h3 id="org8f5b230"><span class="section-number-3">3.5</span> Compare FIR and H-Infinity Filters</h3>
<div class="outline-text-3" id="text-3-5">
<p>
Let&rsquo;s now compare the FIR filters designed in (<a href="#citeproc_bib_item_1">Hua 2005</a>) and the one obtained with the \(\mathcal{H}_\infty\) synthesis on figure <a href="#org9922782">12</a>.
Let&rsquo;s now compare the FIR filters designed in (<a href="#citeproc_bib_item_1">Hua 2005</a>) and the one obtained with the \(\mathcal{H}_\infty\) synthesis on figure <a href="#orga9b5d65">12</a>.
</p>
<div id="org9922782" class="figure">
<div id="orga9b5d65" class="figure">
<p><img src="figs/comp_fir_ligo_hinf.png" alt="comp_fir_ligo_hinf.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Comparison between the FIR filters developped for LIGO and the \(\mathcal{H}_\infty\) complementary filters (<a href="./figs/comp_fir_ligo_hinf.png">png</a>, <a href="./figs/comp_fir_ligo_hinf.pdf">pdf</a>)</p>
@ -786,7 +793,7 @@ Let&rsquo;s now compare the FIR filters designed in (<a href="#citeproc_bib_item
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-07-16 jeu. 14:54</p>
<p class="date">Created: 2020-07-16 jeu. 14:59</p>
</div>
</body>
</html>

10
matlab/index.org
View File

@ -33,9 +33,13 @@ One use of complementary filter is described below:
To achieve this, the sensors included in the filter should complement one another by performing better over specific parts of the system bandwidth.
#+end_quote
- in section [[sec:h_inf_synthesis_complementary_filters]], the $\mathcal{H}_\infty$ synthesis is used for generating two complementary filters ([[file:matlab/h_inf_synthesis_complementary_filters.m][matlab code]])
- in section [[sec:three_comp_filters]], a method using the $\mathcal{H}_\infty$ synthesis is proposed to shape three of more complementary filters ([[file:matlab/three_comp_filters.m][matlab code]])
- in section [[sec:comp_filters_ligo]], the $\mathcal{H}_\infty$ synthesis is used and compared with FIR complementary filters used for LIGO ([[file:matlab/comp_filters_ligo.m][matlab code]])
- in section [[sec:h_inf_synthesis_complementary_filters]], the $\mathcal{H}_\infty$ synthesis is used for generating two complementary filters
- in section [[sec:three_comp_filters]], a method using the $\mathcal{H}_\infty$ synthesis is proposed to shape three of more complementary filters
- in section [[sec:comp_filters_ligo]], the $\mathcal{H}_\infty$ synthesis is used and compared with FIR complementary filters used for LIGO
#+begin_note
Add the Matlab code use to obtain the results presented in the paper are accessible [[file:matlab.zip][here]] and presented below.
#+end_note
* H-Infinity synthesis of complementary filters
:PROPERTIES:

BIN
matlab/matlab.zip Normal file
View File

Binary file not shown.