Add link to home
This commit is contained in:
parent
a865af66ce
commit
ab6a751f5f
194
index.html
194
index.html
@ -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>
|
||||
<!-- 2020-10-26 lun. 14:03 -->
|
||||
<!-- 2020-10-29 jeu. 10:09 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>List of filters - Matlab Implementation</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@ -26,78 +26,78 @@
|
||||
</head>
|
||||
<body>
|
||||
<div id="org-div-home-and-up">
|
||||
<a accesskey="h" href="./index.html"> UP </a>
|
||||
<a accesskey="h" href="../index.html"> UP </a>
|
||||
|
|
||||
<a accesskey="H" href="./index.html"> HOME </a>
|
||||
<a accesskey="H" href="../index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">List of filters - Matlab Implementation</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgb83f79c">1. Low Pass</a>
|
||||
<li><a href="#org580fffb">1. Low Pass</a>
|
||||
<ul>
|
||||
<li><a href="#orgd88840c">1.1. First Order Low Pass Filter</a></li>
|
||||
<li><a href="#org0938139">1.2. Second Order</a></li>
|
||||
<li><a href="#orge580369">1.3. Combine multiple first order filters</a></li>
|
||||
<li><a href="#org407f734">1.1. First Order Low Pass Filter</a></li>
|
||||
<li><a href="#org2414a25">1.2. Second Order</a></li>
|
||||
<li><a href="#orgfb40d54">1.3. Combine multiple first order filters</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org8c4f98e">2. High Pass</a>
|
||||
<li><a href="#org7d2ccd5">2. High Pass</a>
|
||||
<ul>
|
||||
<li><a href="#org946fda0">2.1. First Order</a></li>
|
||||
<li><a href="#orgdb3a46a">2.2. Second Order</a></li>
|
||||
<li><a href="#org81b8ec1">2.3. Combine multiple filters</a></li>
|
||||
<li><a href="#orgcb3470e">2.1. First Order</a></li>
|
||||
<li><a href="#orgeaaee1d">2.2. Second Order</a></li>
|
||||
<li><a href="#org7f499ff">2.3. Combine multiple filters</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org9a4d9f1">3. Band Pass</a>
|
||||
<li><a href="#org5678356">3. Band Pass</a>
|
||||
<ul>
|
||||
<li><a href="#orgb93eef3">3.1. Second Order</a></li>
|
||||
<li><a href="#org8717dd0">3.1. Second Order</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org06d380e">4. Notch</a>
|
||||
<li><a href="#org5e9ca85">4. Notch</a>
|
||||
<ul>
|
||||
<li><a href="#org064544f">4.1. Second Order</a></li>
|
||||
<li><a href="#org768f6c2">4.1. Second Order</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org745749b">5. Chebyshev</a>
|
||||
<li><a href="#orge2713ac">5. Chebyshev</a>
|
||||
<ul>
|
||||
<li><a href="#orgdb4d414">5.1. Chebyshev Type I</a></li>
|
||||
<li><a href="#org171db68">5.1. Chebyshev Type I</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org42f9bf3">6. Lead - Lag</a>
|
||||
<li><a href="#org22f67c7">6. Lead - Lag</a>
|
||||
<ul>
|
||||
<li><a href="#org0cb85e5">6.1. Lead</a></li>
|
||||
<li><a href="#org19e9264">6.2. Lag</a></li>
|
||||
<li><a href="#org15c6b6a">6.1. Lead</a></li>
|
||||
<li><a href="#org1c67cbf">6.2. Lag</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org15058b6">7. Complementary</a></li>
|
||||
<li><a href="#org2d03ba9">8. Performance Weight</a>
|
||||
<li><a href="#org5824a84">7. Complementary</a></li>
|
||||
<li><a href="#org738f16d">8. Performance Weight</a>
|
||||
<ul>
|
||||
<li><a href="#orge550845">8.1. Nice combination</a></li>
|
||||
<li><a href="#org6202dd8">8.2. Alternative</a></li>
|
||||
<li><a href="#orgaa274fe">8.1. Nice combination</a></li>
|
||||
<li><a href="#org9c5eb04">8.2. Alternative</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org5e21f67">9. Combine Filters</a>
|
||||
<li><a href="#org0c47683">9. Combine Filters</a>
|
||||
<ul>
|
||||
<li><a href="#orga943d8f">9.1. Additive</a></li>
|
||||
<li><a href="#org6cc036a">9.2. Multiplicative</a></li>
|
||||
<li><a href="#org61b1c81">9.1. Additive</a></li>
|
||||
<li><a href="#orgeef5af6">9.2. Multiplicative</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org80b3ca3">10. Filters representing noise</a>
|
||||
<li><a href="#org011f201">10. Filters representing noise</a>
|
||||
<ul>
|
||||
<li><a href="#org579591f">10.1. First Order Low Pass Filter</a></li>
|
||||
<li><a href="#orgd4fd858">10.1. First Order Low Pass Filter</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb83f79c" class="outline-2">
|
||||
<h2 id="orgb83f79c"><span class="section-number-2">1</span> Low Pass</h2>
|
||||
<div id="outline-container-org580fffb" class="outline-2">
|
||||
<h2 id="org580fffb"><span class="section-number-2">1</span> Low Pass</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
</div>
|
||||
<div id="outline-container-orgd88840c" class="outline-3">
|
||||
<h3 id="orgd88840c"><span class="section-number-3">1.1</span> First Order Low Pass Filter</h3>
|
||||
<div id="outline-container-org407f734" class="outline-3">
|
||||
<h3 id="org407f734"><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 +129,7 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org65bce28" class="figure">
|
||||
<div id="org47108f3" class="figure">
|
||||
<p><img src="figs/filter_low_pass_first_order.png" alt="filter_low_pass_first_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -137,8 +137,8 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org0938139" class="outline-3">
|
||||
<h3 id="org0938139"><span class="section-number-3">1.2</span> Second Order</h3>
|
||||
<div id="outline-container-org2414a25" class="outline-3">
|
||||
<h3 id="org2414a25"><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 +172,15 @@ H = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3d51d53" class="figure">
|
||||
<div id="org7ef70c6" 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-orge580369" class="outline-3">
|
||||
<h3 id="orge580369"><span class="section-number-3">1.3</span> Combine multiple first order filters</h3>
|
||||
<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 class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
\[ H(s) = \left( \frac{1}{1 + s/\omega_0} \right)^n \]
|
||||
@ -198,7 +198,7 @@ H = (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span c
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org03c708d" class="figure">
|
||||
<div id="org5facb77" 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 +206,12 @@ H = (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8c4f98e" class="outline-2">
|
||||
<h2 id="org8c4f98e"><span class="section-number-2">2</span> High Pass</h2>
|
||||
<div id="outline-container-org7d2ccd5" class="outline-2">
|
||||
<h2 id="org7d2ccd5"><span class="section-number-2">2</span> High Pass</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
</div>
|
||||
<div id="outline-container-org946fda0" class="outline-3">
|
||||
<h3 id="org946fda0"><span class="section-number-3">2.1</span> First Order</h3>
|
||||
<div id="outline-container-orgcb3470e" class="outline-3">
|
||||
<h3 id="orgcb3470e"><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 +243,15 @@ H = (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org5e8496d" class="figure">
|
||||
<div id="orge0525b5" 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-orgdb3a46a" class="outline-3">
|
||||
<h3 id="orgdb3a46a"><span class="section-number-3">2.2</span> Second Order</h3>
|
||||
<div id="outline-container-orgeaaee1d" class="outline-3">
|
||||
<h3 id="orgeaaee1d"><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 +277,15 @@ H = (s<span class="org-type">^</span>2<span class="org-type">/</span>w0<span cla
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga48ef87" class="figure">
|
||||
<div id="org3651b21" 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-org81b8ec1" class="outline-3">
|
||||
<h3 id="org81b8ec1"><span class="section-number-3">2.3</span> Combine multiple filters</h3>
|
||||
<div id="outline-container-org7f499ff" class="outline-3">
|
||||
<h3 id="org7f499ff"><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 +303,7 @@ H = ((s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org99826f5" class="figure">
|
||||
<div id="org6f8e2de" 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 +311,21 @@ H = ((s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9a4d9f1" class="outline-2">
|
||||
<h2 id="org9a4d9f1"><span class="section-number-2">3</span> Band Pass</h2>
|
||||
<div id="outline-container-org5678356" class="outline-2">
|
||||
<h2 id="org5678356"><span class="section-number-2">3</span> Band Pass</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-orgb93eef3" class="outline-3">
|
||||
<h3 id="orgb93eef3"><span class="section-number-3">3.1</span> Second Order</h3>
|
||||
<div id="outline-container-org8717dd0" class="outline-3">
|
||||
<h3 id="org8717dd0"><span class="section-number-3">3.1</span> Second Order</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org06d380e" class="outline-2">
|
||||
<h2 id="org06d380e"><span class="section-number-2">4</span> Notch</h2>
|
||||
<div id="outline-container-org5e9ca85" class="outline-2">
|
||||
<h2 id="org5e9ca85"><span class="section-number-2">4</span> Notch</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org064544f" class="outline-3">
|
||||
<h3 id="org064544f"><span class="section-number-3">4.1</span> Second Order</h3>
|
||||
<div id="outline-container-org768f6c2" class="outline-3">
|
||||
<h3 id="org768f6c2"><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 +353,13 @@ H = (s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgba70cf5" class="figure">
|
||||
<div id="org4faffaa" class="figure">
|
||||
<p><img src="figs/filter_notch_xi.png" alt="filter_notch_xi.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga3207e8" class="figure">
|
||||
<div id="org1272339" class="figure">
|
||||
<p><img src="figs/filter_notch_gc.png" alt="filter_notch_gc.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -367,12 +367,12 @@ H = (s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org745749b" class="outline-2">
|
||||
<h2 id="org745749b"><span class="section-number-2">5</span> Chebyshev</h2>
|
||||
<div id="outline-container-orge2713ac" class="outline-2">
|
||||
<h2 id="orge2713ac"><span class="section-number-2">5</span> Chebyshev</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-orgdb4d414" class="outline-3">
|
||||
<h3 id="orgdb4d414"><span class="section-number-3">5.1</span> Chebyshev Type I</h3>
|
||||
<div id="outline-container-org171db68" class="outline-3">
|
||||
<h3 id="org171db68"><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 +387,12 @@ H = ss(A, B, C, D);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org42f9bf3" class="outline-2">
|
||||
<h2 id="org42f9bf3"><span class="section-number-2">6</span> Lead - Lag</h2>
|
||||
<div id="outline-container-org22f67c7" class="outline-2">
|
||||
<h2 id="org22f67c7"><span class="section-number-2">6</span> Lead - Lag</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org0cb85e5" class="outline-3">
|
||||
<h3 id="org0cb85e5"><span class="section-number-3">6.1</span> Lead</h3>
|
||||
<div id="outline-container-org15c6b6a" class="outline-3">
|
||||
<h3 id="org15c6b6a"><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 +412,7 @@ 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="#org6e073c7">10</a>):
|
||||
<li>the phase lead at \(\omega_c\) is equal to (Figure <a href="#org35d4f5a">10</a>):
|
||||
\[ \angle H(j\omega_c) = \tan^{-1}(\sqrt{a}) - \tan^{-1}(1/\sqrt{a}) \]</li>
|
||||
</ul>
|
||||
|
||||
@ -428,21 +428,21 @@ H = (1 <span class="org-type">+</span> s<span class="org-type">/</span>(wc<span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf77036f" class="figure">
|
||||
<div id="orgdc2e657" class="figure">
|
||||
<p><img src="figs/filter_lead.png" alt="filter_lead.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6e073c7" class="figure">
|
||||
<div id="org35d4f5a" 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-org19e9264" class="outline-3">
|
||||
<h3 id="org19e9264"><span class="section-number-3">6.2</span> Lag</h3>
|
||||
<div id="outline-container-org1c67cbf" class="outline-3">
|
||||
<h3 id="org1c67cbf"><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 +462,7 @@ 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="#orge3aeee4">12</a>):
|
||||
<li>the phase lag at \(\omega_c\) is equal to (Figure <a href="#org013fbcc">12</a>):
|
||||
\[ \angle H(j\omega_c) = \tan^{-1}(1/\sqrt{a}) - \tan^{-1}(\sqrt{a}) \]</li>
|
||||
</ul>
|
||||
|
||||
@ -478,13 +478,13 @@ H = (wc<span class="org-type">*</span>sqrt(a) <span class="org-type">+</span> s)
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgcb08a98" class="figure">
|
||||
<div id="org7dff5fa" class="figure">
|
||||
<p><img src="figs/filter_lag.png" alt="filter_lag.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge3aeee4" class="figure">
|
||||
<div id="org013fbcc" class="figure">
|
||||
<p><img src="figs/filter_lag_effect_a_phase.png" alt="filter_lag_effect_a_phase.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -492,16 +492,16 @@ H = (wc<span class="org-type">*</span>sqrt(a) <span class="org-type">+</span> s)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org15058b6" class="outline-2">
|
||||
<h2 id="org15058b6"><span class="section-number-2">7</span> Complementary</h2>
|
||||
<div id="outline-container-org5824a84" class="outline-2">
|
||||
<h2 id="org5824a84"><span class="section-number-2">7</span> Complementary</h2>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2d03ba9" class="outline-2">
|
||||
<h2 id="org2d03ba9"><span class="section-number-2">8</span> Performance Weight</h2>
|
||||
<div id="outline-container-org738f16d" class="outline-2">
|
||||
<h2 id="org738f16d"><span class="section-number-2">8</span> Performance Weight</h2>
|
||||
<div class="outline-text-2" id="text-8">
|
||||
</div>
|
||||
<div id="outline-container-orge550845" class="outline-3">
|
||||
<h3 id="orge550845"><span class="section-number-3">8.1</span> Nice combination</h3>
|
||||
<div id="outline-container-orgaa274fe" class="outline-3">
|
||||
<h3 id="orgaa274fe"><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 +520,8 @@ wH = Gc<span class="org-type">*</span>(((G1<span class="org-type">/</span>Gc)<sp
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org6202dd8" class="outline-3">
|
||||
<h3 id="org6202dd8"><span class="section-number-3">8.2</span> Alternative</h3>
|
||||
<div id="outline-container-org9c5eb04" class="outline-3">
|
||||
<h3 id="org9c5eb04"><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 +533,7 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org503aff1" class="figure">
|
||||
<div id="org67210d5" class="figure">
|
||||
<p><img src="figs/weight_first_order.png" alt="weight_first_order.png" />
|
||||
</p>
|
||||
</div>
|
||||
@ -541,12 +541,12 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5e21f67" class="outline-2">
|
||||
<h2 id="org5e21f67"><span class="section-number-2">9</span> Combine Filters</h2>
|
||||
<div id="outline-container-org0c47683" class="outline-2">
|
||||
<h2 id="org0c47683"><span class="section-number-2">9</span> Combine Filters</h2>
|
||||
<div class="outline-text-2" id="text-9">
|
||||
</div>
|
||||
<div id="outline-container-orga943d8f" class="outline-3">
|
||||
<h3 id="orga943d8f"><span class="section-number-3">9.1</span> Additive</h3>
|
||||
<div id="outline-container-org61b1c81" class="outline-3">
|
||||
<h3 id="org61b1c81"><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 +554,12 @@ H = (s<span class="org-type">/</span>sqrt(M) <span class="org-type">+</span> w0)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6cc036a" class="outline-3">
|
||||
<h3 id="org6cc036a"><span class="section-number-3">9.2</span> Multiplicative</h3>
|
||||
<div id="outline-container-orgeef5af6" class="outline-3">
|
||||
<h3 id="orgeef5af6"><span class="section-number-3">9.2</span> Multiplicative</h3>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org80b3ca3" class="outline-2">
|
||||
<h2 id="org80b3ca3"><span class="section-number-2">10</span> Filters representing noise</h2>
|
||||
<div id="outline-container-org011f201" class="outline-2">
|
||||
<h2 id="org011f201"><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 +577,8 @@ And the root mean square (RMS) of \(n(t)\) is:
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org579591f" class="outline-3">
|
||||
<h3 id="org579591f"><span class="section-number-3">10.1</span> First Order Low Pass Filter</h3>
|
||||
<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 class="outline-text-3" id="text-10-1">
|
||||
<p>
|
||||
\[ G(s) = \frac{g_0}{1 + \frac{s}{\omega_c}} \]
|
||||
@ -646,7 +646,7 @@ 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: 2020-10-26 lun. 14:03</p>
|
||||
<p class="date">Created: 2020-10-29 jeu. 10:09</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -4,8 +4,8 @@
|
||||
#+EMAIL: dehaeze.thomas@gmail.com
|
||||
#+AUTHOR: Dehaeze Thomas
|
||||
|
||||
#+HTML_LINK_HOME: ./index.html
|
||||
#+HTML_LINK_UP: ./index.html
|
||||
#+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"/>
|
||||
|
||||
Loading…
Reference in New Issue
Block a user