Use online CSS and JS
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-10-29 jeu. 10:09 -->
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<!-- 2020-11-12 jeu. 10:35 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>List of filters - Matlab Implementation</title>
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<title>Bank of Linear Filters - Matlab</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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<link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
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<script type="text/javascript" src="./js/jquery.min.js"></script>
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<script type="text/javascript" src="./js/bootstrap.min.js"></script>
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<script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
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<script type="text/javascript" src="./js/readtheorg.js"></script>
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<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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<script>MathJax = {
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tex: {
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tags: 'ams',
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">List of filters - Matlab Implementation</h1>
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<h1 class="title">Bank of Linear Filters - Matlab</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org580fffb">1. Low Pass</a>
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<li><a href="#org90266e3">1. Low Pass</a>
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<ul>
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<li><a href="#org407f734">1.1. First Order Low Pass Filter</a></li>
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<li><a href="#org2414a25">1.2. Second Order</a></li>
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<li><a href="#orgfb40d54">1.3. Combine multiple first order filters</a></li>
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<li><a href="#org4291475">1.1. First Order Low Pass Filter</a></li>
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<li><a href="#org88f266d">1.2. Second Order</a></li>
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<li><a href="#org1ee2123">1.3. Combine multiple first order filters</a></li>
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</ul>
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</li>
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<li><a href="#org7d2ccd5">2. High Pass</a>
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<li><a href="#orgd7f4531">2. High Pass</a>
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<ul>
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<li><a href="#orgcb3470e">2.1. First Order</a></li>
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<li><a href="#orgeaaee1d">2.2. Second Order</a></li>
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<li><a href="#org7f499ff">2.3. Combine multiple filters</a></li>
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<li><a href="#org5859621">2.1. First Order</a></li>
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<li><a href="#org988fb36">2.2. Second Order</a></li>
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<li><a href="#orgd1ae949">2.3. Combine multiple filters</a></li>
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</ul>
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</li>
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<li><a href="#org5678356">3. Band Pass</a>
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<li><a href="#org0871964">3. Band Pass</a>
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<ul>
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<li><a href="#org8717dd0">3.1. Second Order</a></li>
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<li><a href="#org020bd3f">3.1. Second Order</a></li>
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</ul>
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</li>
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<li><a href="#org5e9ca85">4. Notch</a>
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<li><a href="#org226333f">4. Notch</a>
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<ul>
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<li><a href="#org768f6c2">4.1. Second Order</a></li>
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<li><a href="#org5d6517b">4.1. Second Order</a></li>
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</ul>
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</li>
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<li><a href="#orge2713ac">5. Chebyshev</a>
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<li><a href="#orgff2aff5">5. Chebyshev</a>
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<ul>
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<li><a href="#org171db68">5.1. Chebyshev Type I</a></li>
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<li><a href="#orgb7b715f">5.1. Chebyshev Type I</a></li>
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</ul>
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</li>
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<li><a href="#org22f67c7">6. Lead - Lag</a>
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<li><a href="#orge46a59c">6. Lead - Lag</a>
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<ul>
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<li><a href="#org15c6b6a">6.1. Lead</a></li>
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<li><a href="#org1c67cbf">6.2. Lag</a></li>
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<li><a href="#org6336fc3">6.1. Lead</a></li>
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<li><a href="#org3797972">6.2. Lag</a></li>
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</ul>
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</li>
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<li><a href="#org5824a84">7. Complementary</a></li>
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<li><a href="#org738f16d">8. Performance Weight</a>
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<li><a href="#org5e67a97">7. Complementary</a></li>
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<li><a href="#org74fba97">8. Performance Weight</a>
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<ul>
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<li><a href="#orgaa274fe">8.1. Nice combination</a></li>
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<li><a href="#org9c5eb04">8.2. Alternative</a></li>
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<li><a href="#org64d3111">8.1. Nice combination</a></li>
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<li><a href="#org978d37b">8.2. Alternative</a></li>
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</ul>
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</li>
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<li><a href="#org0c47683">9. Combine Filters</a>
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<li><a href="#org043cd0b">9. Combine Filters</a>
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<ul>
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<li><a href="#org61b1c81">9.1. Additive</a></li>
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<li><a href="#orgeef5af6">9.2. Multiplicative</a></li>
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<li><a href="#orgbb8d210">9.1. Additive</a></li>
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<li><a href="#orgc6eac8f">9.2. Multiplicative</a></li>
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</ul>
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</li>
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<li><a href="#org011f201">10. Filters representing noise</a>
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<li><a href="#org2616858">10. Filters representing noise</a>
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<ul>
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<li><a href="#orgd4fd858">10.1. First Order Low Pass Filter</a></li>
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<li><a href="#orgb12ce21">10.1. First Order Low Pass Filter</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org580fffb" class="outline-2">
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<h2 id="org580fffb"><span class="section-number-2">1</span> Low Pass</h2>
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<div id="outline-container-org90266e3" class="outline-2">
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<h2 id="org90266e3"><span class="section-number-2">1</span> Low Pass</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org407f734" class="outline-3">
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<h3 id="org407f734"><span class="section-number-3">1.1</span> First Order Low Pass Filter</h3>
|
||||
<div id="outline-container-org4291475" class="outline-3">
|
||||
<h3 id="org4291475"><span class="section-number-3">1.1</span> First Order Low Pass Filter</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
\[ H(s) = \frac{1}{1 + s/\omega_0} \]
|
||||
@ -129,7 +124,7 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org47108f3" class="figure">
|
||||
<div id="org3a9bd55" class="figure">
|
||||
<p><img src="figs/filter_low_pass_first_order.png" alt="filter_low_pass_first_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -137,8 +132,8 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org2414a25" class="outline-3">
|
||||
<h3 id="org2414a25"><span class="section-number-3">1.2</span> Second Order</h3>
|
||||
<div id="outline-container-org88f266d" class="outline-3">
|
||||
<h3 id="org88f266d"><span class="section-number-3">1.2</span> Second Order</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
\[ H(s) = \frac{1}{1 + 2 \xi / \omega_0 s + s^2/\omega_0^2} \]
|
||||
@ -172,15 +167,15 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7ef70c6" class="figure">
|
||||
<div id="org666b377" class="figure">
|
||||
<p><img src="figs/filter_low_pass_second_order.png" alt="filter_low_pass_second_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfb40d54" class="outline-3">
|
||||
<h3 id="orgfb40d54"><span class="section-number-3">1.3</span> Combine multiple first order filters</h3>
|
||||
<div id="outline-container-org1ee2123" class="outline-3">
|
||||
<h3 id="org1ee2123"><span class="section-number-3">1.3</span> Combine multiple first order filters</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
\[ H(s) = \left( \frac{1}{1 + s/\omega_0} \right)^n \]
|
||||
@ -198,7 +193,7 @@ H = (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span c
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org5facb77" class="figure">
|
||||
<div id="orgb9222b5" class="figure">
|
||||
<p><img src="figs/filter_low_pass_first_order_add.png" alt="filter_low_pass_first_order_add.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -206,12 +201,12 @@ H = (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7d2ccd5" class="outline-2">
|
||||
<h2 id="org7d2ccd5"><span class="section-number-2">2</span> High Pass</h2>
|
||||
<div id="outline-container-orgd7f4531" class="outline-2">
|
||||
<h2 id="orgd7f4531"><span class="section-number-2">2</span> High Pass</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
</div>
|
||||
<div id="outline-container-orgcb3470e" class="outline-3">
|
||||
<h3 id="orgcb3470e"><span class="section-number-3">2.1</span> First Order</h3>
|
||||
<div id="outline-container-org5859621" class="outline-3">
|
||||
<h3 id="org5859621"><span class="section-number-3">2.1</span> First Order</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
\[ H(s) = \frac{s/\omega_0}{1 + s/\omega_0} \]
|
||||
@ -243,15 +238,15 @@ H = (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge0525b5" class="figure">
|
||||
<div id="org422aab2" class="figure">
|
||||
<p><img src="figs/filter_high_pass_first_order.png" alt="filter_high_pass_first_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgeaaee1d" class="outline-3">
|
||||
<h3 id="orgeaaee1d"><span class="section-number-3">2.2</span> Second Order</h3>
|
||||
<div id="outline-container-org988fb36" class="outline-3">
|
||||
<h3 id="org988fb36"><span class="section-number-3">2.2</span> Second Order</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
\[ H(s) = \frac{s^2/\omega_0^2}{1 + 2 \xi / \omega_0 s + s^2/\omega_0^2} \]
|
||||
@ -277,15 +272,15 @@ H = (s<span class="org-type">^</span>2<span class="org-type">/</span>w0<span cla
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3651b21" class="figure">
|
||||
<div id="org66dc7df" class="figure">
|
||||
<p><img src="figs/filter_high_pass_second_order.png" alt="filter_high_pass_second_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7f499ff" class="outline-3">
|
||||
<h3 id="org7f499ff"><span class="section-number-3">2.3</span> Combine multiple filters</h3>
|
||||
<div id="outline-container-orgd1ae949" class="outline-3">
|
||||
<h3 id="orgd1ae949"><span class="section-number-3">2.3</span> Combine multiple filters</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
\[ H(s) = \left( \frac{s/\omega_0}{1 + s/\omega_0} \right)^n \]
|
||||
@ -303,7 +298,7 @@ H = ((s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6f8e2de" class="figure">
|
||||
<div id="orgc70858b" class="figure">
|
||||
<p><img src="figs/filter_high_pass_first_order_add.png" alt="filter_high_pass_first_order_add.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -311,21 +306,21 @@ H = ((s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5678356" class="outline-2">
|
||||
<h2 id="org5678356"><span class="section-number-2">3</span> Band Pass</h2>
|
||||
<div id="outline-container-org0871964" class="outline-2">
|
||||
<h2 id="org0871964"><span class="section-number-2">3</span> Band Pass</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-org8717dd0" class="outline-3">
|
||||
<h3 id="org8717dd0"><span class="section-number-3">3.1</span> Second Order</h3>
|
||||
<div id="outline-container-org020bd3f" class="outline-3">
|
||||
<h3 id="org020bd3f"><span class="section-number-3">3.1</span> Second Order</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5e9ca85" class="outline-2">
|
||||
<h2 id="org5e9ca85"><span class="section-number-2">4</span> Notch</h2>
|
||||
<div id="outline-container-org226333f" class="outline-2">
|
||||
<h2 id="org226333f"><span class="section-number-2">4</span> Notch</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org768f6c2" class="outline-3">
|
||||
<h3 id="org768f6c2"><span class="section-number-3">4.1</span> Second Order</h3>
|
||||
<div id="outline-container-org5d6517b" class="outline-3">
|
||||
<h3 id="org5d6517b"><span class="section-number-3">4.1</span> Second Order</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
\begin{equation}
|
||||
\frac{s^2 + 2 g_c \xi \omega_n s + \omega_n^2}{s^2 + 2 \xi \omega_n s + \omega_n^2}
|
||||
@ -353,13 +348,13 @@ H = (s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org4faffaa" class="figure">
|
||||
<div id="orgbb197d6" class="figure">
|
||||
<p><img src="figs/filter_notch_xi.png" alt="filter_notch_xi.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org1272339" class="figure">
|
||||
<div id="org5b3ff85" class="figure">
|
||||
<p><img src="figs/filter_notch_gc.png" alt="filter_notch_gc.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -367,12 +362,12 @@ H = (s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge2713ac" class="outline-2">
|
||||
<h2 id="orge2713ac"><span class="section-number-2">5</span> Chebyshev</h2>
|
||||
<div id="outline-container-orgff2aff5" class="outline-2">
|
||||
<h2 id="orgff2aff5"><span class="section-number-2">5</span> Chebyshev</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-org171db68" class="outline-3">
|
||||
<h3 id="org171db68"><span class="section-number-3">5.1</span> Chebyshev Type I</h3>
|
||||
<div id="outline-container-orgb7b715f" class="outline-3">
|
||||
<h3 id="orgb7b715f"><span class="section-number-3">5.1</span> Chebyshev Type I</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">n = 4; <span class="org-comment">% Order of the filter</span>
|
||||
@ -387,12 +382,12 @@ H = ss(A, B, C, D);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org22f67c7" class="outline-2">
|
||||
<h2 id="org22f67c7"><span class="section-number-2">6</span> Lead - Lag</h2>
|
||||
<div id="outline-container-orge46a59c" class="outline-2">
|
||||
<h2 id="orge46a59c"><span class="section-number-2">6</span> Lead - Lag</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org15c6b6a" class="outline-3">
|
||||
<h3 id="org15c6b6a"><span class="section-number-3">6.1</span> Lead</h3>
|
||||
<div id="outline-container-org6336fc3" class="outline-3">
|
||||
<h3 id="org6336fc3"><span class="section-number-3">6.1</span> Lead</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
\begin{equation}
|
||||
H(s) = \frac{1 + \frac{s}{w_c/\sqrt{a}}}{1 + \frac{s}{w_c \sqrt{a}}}, \quad a > 1
|
||||
@ -412,7 +407,7 @@ Characteristics:
|
||||
<ul class="org-ul">
|
||||
<li>the low frequency gain is \(1\)</li>
|
||||
<li>the high frequency gain is \(a\)</li>
|
||||
<li>the phase lead at \(\omega_c\) is equal to (Figure <a href="#org35d4f5a">10</a>):
|
||||
<li>the phase lead at \(\omega_c\) is equal to (Figure <a href="#orgefcd37b">10</a>):
|
||||
\[ \angle H(j\omega_c) = \tan^{-1}(\sqrt{a}) - \tan^{-1}(1/\sqrt{a}) \]</li>
|
||||
</ul>
|
||||
|
||||
@ -428,21 +423,21 @@ H = (1 <span class="org-type">+</span> s<span class="org-type">/</span>(wc<span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgdc2e657" class="figure">
|
||||
<div id="orga3b4f13" class="figure">
|
||||
<p><img src="figs/filter_lead.png" alt="filter_lead.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org35d4f5a" class="figure">
|
||||
<div id="orgefcd37b" class="figure">
|
||||
<p><img src="figs/filter_lead_effect_a_phase.png" alt="filter_lead_effect_a_phase.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1c67cbf" class="outline-3">
|
||||
<h3 id="org1c67cbf"><span class="section-number-3">6.2</span> Lag</h3>
|
||||
<div id="outline-container-org3797972" class="outline-3">
|
||||
<h3 id="org3797972"><span class="section-number-3">6.2</span> Lag</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
\begin{equation}
|
||||
H(s) = \frac{w_c \sqrt{a} + s}{\frac{w_c}{\sqrt{a}} + s}, \quad a > 1
|
||||
@ -462,7 +457,7 @@ Characteristics:
|
||||
<ul class="org-ul">
|
||||
<li>the low frequency gain is increased by a factor \(a\)</li>
|
||||
<li>the high frequency gain is \(1\) (unchanged)</li>
|
||||
<li>the phase lag at \(\omega_c\) is equal to (Figure <a href="#org013fbcc">12</a>):
|
||||
<li>the phase lag at \(\omega_c\) is equal to (Figure <a href="#orgbed77d1">12</a>):
|
||||
\[ \angle H(j\omega_c) = \tan^{-1}(1/\sqrt{a}) - \tan^{-1}(\sqrt{a}) \]</li>
|
||||
</ul>
|
||||
|
||||
@ -478,13 +473,13 @@ H = (wc<span class="org-type">*</span>sqrt(a) <span class="org-type">+</span> s)
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7dff5fa" class="figure">
|
||||
<div id="orgce1450b" class="figure">
|
||||
<p><img src="figs/filter_lag.png" alt="filter_lag.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org013fbcc" class="figure">
|
||||
<div id="orgbed77d1" class="figure">
|
||||
<p><img src="figs/filter_lag_effect_a_phase.png" alt="filter_lag_effect_a_phase.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -492,16 +487,16 @@ H = (wc<span class="org-type">*</span>sqrt(a) <span class="org-type">+</span> s)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5824a84" class="outline-2">
|
||||
<h2 id="org5824a84"><span class="section-number-2">7</span> Complementary</h2>
|
||||
<div id="outline-container-org5e67a97" class="outline-2">
|
||||
<h2 id="org5e67a97"><span class="section-number-2">7</span> Complementary</h2>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org738f16d" class="outline-2">
|
||||
<h2 id="org738f16d"><span class="section-number-2">8</span> Performance Weight</h2>
|
||||
<div id="outline-container-org74fba97" class="outline-2">
|
||||
<h2 id="org74fba97"><span class="section-number-2">8</span> Performance Weight</h2>
|
||||
<div class="outline-text-2" id="text-8">
|
||||
</div>
|
||||
<div id="outline-container-orgaa274fe" class="outline-3">
|
||||
<h3 id="orgaa274fe"><span class="section-number-3">8.1</span> Nice combination</h3>
|
||||
<div id="outline-container-org64d3111" class="outline-3">
|
||||
<h3 id="org64d3111"><span class="section-number-3">8.1</span> Nice combination</h3>
|
||||
<div class="outline-text-3" id="text-8-1">
|
||||
\begin{equation}
|
||||
W(s) = G_c * \left(\frac{\frac{1}{\omega_0}\sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{G_0}{G_c}\right)^{\frac{1}{n}}}{\frac{1}{\omega_0} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{\left(\frac{G_\infty}{G_c}\right)^{\frac{2}{n}} - 1}} s + 1}\right)^n
|
||||
@ -520,8 +515,8 @@ wH = Gc<span class="org-type">*</span>(((G1<span class="org-type">/</span>Gc)<sp
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org9c5eb04" class="outline-3">
|
||||
<h3 id="org9c5eb04"><span class="section-number-3">8.2</span> Alternative</h3>
|
||||
<div id="outline-container-org978d37b" class="outline-3">
|
||||
<h3 id="org978d37b"><span class="section-number-3">8.2</span> Alternative</h3>
|
||||
<div class="outline-text-3" id="text-8-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
|
||||
@ -533,7 +528,7 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org67210d5" class="figure">
|
||||
<div id="orgb351bf7" class="figure">
|
||||
<p><img src="figs/weight_first_order.png" alt="weight_first_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -541,12 +536,12 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c47683" class="outline-2">
|
||||
<h2 id="org0c47683"><span class="section-number-2">9</span> Combine Filters</h2>
|
||||
<div id="outline-container-org043cd0b" class="outline-2">
|
||||
<h2 id="org043cd0b"><span class="section-number-2">9</span> Combine Filters</h2>
|
||||
<div class="outline-text-2" id="text-9">
|
||||
</div>
|
||||
<div id="outline-container-org61b1c81" class="outline-3">
|
||||
<h3 id="org61b1c81"><span class="section-number-3">9.1</span> Additive</h3>
|
||||
<div id="outline-container-orgbb8d210" class="outline-3">
|
||||
<h3 id="orgbb8d210"><span class="section-number-3">9.1</span> Additive</h3>
|
||||
<div class="outline-text-3" id="text-9-1">
|
||||
<ul class="org-ul">
|
||||
<li class="off"><code>[ ]</code> Explain how phase and magnitude combine</li>
|
||||
@ -554,12 +549,12 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgeef5af6" class="outline-3">
|
||||
<h3 id="orgeef5af6"><span class="section-number-3">9.2</span> Multiplicative</h3>
|
||||
<div id="outline-container-orgc6eac8f" class="outline-3">
|
||||
<h3 id="orgc6eac8f"><span class="section-number-3">9.2</span> Multiplicative</h3>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org011f201" class="outline-2">
|
||||
<h2 id="org011f201"><span class="section-number-2">10</span> Filters representing noise</h2>
|
||||
<div id="outline-container-org2616858" class="outline-2">
|
||||
<h2 id="org2616858"><span class="section-number-2">10</span> Filters representing noise</h2>
|
||||
<div class="outline-text-2" id="text-10">
|
||||
<p>
|
||||
Let’s consider a noise \(n\) that is shaped from a white-noise \(\tilde{n}\) with unitary PSD (\(\Phi_\tilde{n}(\omega) = 1\)) using a transfer function \(G(s)\).
|
||||
@ -577,8 +572,8 @@ And the root mean square (RMS) of \(n(t)\) is:
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd4fd858" class="outline-3">
|
||||
<h3 id="orgd4fd858"><span class="section-number-3">10.1</span> First Order Low Pass Filter</h3>
|
||||
<div id="outline-container-orgb12ce21" class="outline-3">
|
||||
<h3 id="orgb12ce21"><span class="section-number-3">10.1</span> First Order Low Pass Filter</h3>
|
||||
<div class="outline-text-3" id="text-10-1">
|
||||
<p>
|
||||
\[ G(s) = \frac{g_0}{1 + \frac{s}{\omega_c}} \]
|
||||
@ -646,7 +641,7 @@ Thus, if a sensor is said to have a RMS noise of \(\sigma = 10 nm\ rms\) over a
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-10-29 jeu. 10:09</p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 10:35</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
12
index.org
12
index.org
@ -1,4 +1,4 @@
|
||||
#+TITLE: List of filters - Matlab Implementation
|
||||
#+TITLE: Bank of Linear Filters - Matlab
|
||||
:DRAWER:
|
||||
#+LANGUAGE: en
|
||||
#+EMAIL: dehaeze.thomas@gmail.com
|
||||
@ -7,13 +7,8 @@
|
||||
#+HTML_LINK_HOME: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||
|
||||
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
||||
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||
@ -23,6 +18,7 @@
|
||||
#+PROPERTY: header-args:latex+ :eval no-export
|
||||
#+PROPERTY: header-args:latex+ :exports both
|
||||
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||||
#+PROPERTY: header-args:latex+ :tangle no
|
||||
#+PROPERTY: header-args:latex+ :output-dir figs
|
||||
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
||||
|
||||
|
||||
7
js/bootstrap.min.js
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js/bootstrap.min.js
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4
js/jquery.min.js
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js/jquery.min.js
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@ -1,85 +0,0 @@
|
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$(function() {
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$('.note').before("<p class='admonition-title note'>Note</p>");
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$('.seealso').before("<p class='admonition-title seealso'>See also</p>");
|
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$('.warning').before("<p class='admonition-title warning'>Warning</p>");
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$('.caution').before("<p class='admonition-title caution'>Caution</p>");
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$('.hint').before("<p class='admonition-title hint'>Hint</p>");
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$('.error').before("<p class='admonition-title error'>Error</p>");
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$('.danger').before("<p class='admonition-title danger'>Danger</p>");
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});
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$( document ).ready(function() {
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// Shift nav in mobile when clicking the menu.
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$(document).on('click', "[data-toggle='wy-nav-top']", function() {
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$("[data-toggle='wy-nav-shift']").toggleClass("shift");
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$("[data-toggle='rst-versions']").toggleClass("shift");
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$(document).on('click', ".wy-menu-vertical .current ul li a", function() {
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$("[data-toggle='wy-nav-shift']").removeClass("shift");
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$("[data-toggle='rst-versions']").toggleClass("shift");
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$(document).on('click', "[data-toggle='rst-current-version']", function() {
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$("[data-toggle='rst-versions']").toggleClass("shift-up");
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$("table.docutils:not(.field-list)").wrap("<div class='wy-table-responsive'></div>");
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});
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$( document ).ready(function() {
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$('#text-table-of-contents ul').first().addClass('nav');
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// ScrollSpy also requires that we use
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// a Bootstrap nav component.
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$('body').scrollspy({target: '#text-table-of-contents'});
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|
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|
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$('#content').prepend(toggleSidebar);
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// add close button when sidebar showed in mobile screen
|
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var closeBtn = $('<a class="close-sidebar" href="#">Close</a>');
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var tocTitle = $('#table-of-contents').find('h2');
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win.on('resize', applyStickNav);
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navBar = jquery('nav.wy-nav-side:first');
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win = jquery(window);
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|
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jquery(init);
|
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|
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|
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return {
|
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StickyNav : stickyNav
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1001
mat/cheby1_hpf.csv
1001
mat/cheby1_hpf.csv
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1001
mat/lag_filter.csv
1001
mat/lag_filter.csv
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1001
mat/lead_filter.csv
1001
mat/lead_filter.csv
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Loading…
Reference in New Issue
Block a user