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<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="#orgb268523">1. Low Pass</a>
<ul>
<li><a href="#orgc6f2664">1.1. First Order</a></li>
<li><a href="#org9a99d55">1.2. Second Order</a></li>
<li><a href="#org360c529">1.3. Combine multiple filters</a></li>
</ul>
</li>
<li><a href="#orgb54c74e">2. High Pass</a>
<ul>
<li><a href="#orgd3a001c">2.1. First Order</a></li>
<li><a href="#orgbb7602b">2.2. Second Order</a></li>
<li><a href="#org593e27b">2.3. Combine multiple filters</a></li>
</ul>
</li>
<li><a href="#org499bdf6">3. Band Pass</a></li>
<li><a href="#orge29baf7">4. Notch</a></li>
<li><a href="#org55acbde">5. Chebyshev</a>
<ul>
<li><a href="#org04af1b5">5.1. Chebyshev Type I</a></li>
</ul>
</li>
<li><a href="#org214e83b">6. Complementary</a></li>
</ul>
</div>
</div>
<div id="outline-container-orgb268523" class="outline-2">
<h2 id="orgb268523"><span class="section-number-2">1</span> Low Pass</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgc6f2664" class="outline-3">
<h3 id="orgc6f2664"><span class="section-number-3">1.1</span> First Order</h3>
<div class="outline-text-3" id="text-1-1">
<p>
\[ H(s) = \frac{1}{1 + s/\omega_0} \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
H = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgdd885c3" class="figure">
<p><img src="figs/lpf_first_order.png" alt="lpf_first_order.png" />
</p>
<p><span class="figure-number">Figure 1: </span>First Order Low Pass Filter (<a href="./figs/lpf_first_order.png">png</a>, <a href="./figs/lpf_first_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
<div id="outline-container-org9a99d55" class="outline-3">
<h3 id="org9a99d55"><span class="section-number-3">1.2</span> Second Order</h3>
<div class="outline-text-3" id="text-1-2">
<p>
\[ H(s) = \frac{1}{1 + 2 \xi / \omega_0 s + s^2/\omega_0^2} \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
xi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">3</span>;
H = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>xi<span class="org-type">/</span>w0<span class="org-type">*</span>s <span class="org-type">+</span> s<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>w0<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org43d0a1a" class="figure">
<p><img src="figs/lpf_second_order.png" alt="lpf_second_order.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Second Order Low Pass Filter (<a href="./figs/lpf_second_order.png">png</a>, <a href="./figs/lpf_second_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
<div id="outline-container-org360c529" class="outline-3">
<h3 id="org360c529"><span class="section-number-3">1.3</span> Combine multiple filters</h3>
<div class="outline-text-3" id="text-1-3">
<p>
\[ H(s) = \left( \frac{1}{1 + s/\omega_0} \right)^n \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
n = <span class="org-highlight-numbers-number">3</span>;
H = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span>n;
</pre>
</div>
<div id="org63ca6d5" class="figure">
<p><img src="figs/lpf_multiple_first_order.png" alt="lpf_multiple_first_order.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Combine Multiple First Order Low Pass Filter (<a href="./figs/lpf_multiple_first_order.png">png</a>, <a href="./figs/lpf_multiple_first_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgb54c74e" class="outline-2">
<h2 id="orgb54c74e"><span class="section-number-2">2</span> High Pass</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-orgd3a001c" class="outline-3">
<h3 id="orgd3a001c"><span class="section-number-3">2.1</span> First Order</h3>
<div class="outline-text-3" id="text-2-1">
<p>
\[ H(s) = \frac{s/\omega_0}{1 + s/\omega_0} \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
H = <span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orga1cad81" class="figure">
<p><img src="figs/hpf_first_order.png" alt="hpf_first_order.png" />
</p>
<p><span class="figure-number">Figure 4: </span>First Order High Pass Filter (<a href="./figs/hpf_first_order.png">png</a>, <a href="./figs/hpf_first_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
<div id="outline-container-orgbb7602b" class="outline-3">
<h3 id="orgbb7602b"><span class="section-number-3">2.2</span> Second Order</h3>
<div class="outline-text-3" id="text-2-2">
<p>
\[ H(s) = \frac{s^2/\omega_0^2}{1 + 2 \xi / \omega_0 s + s^2/\omega_0^2} \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
xi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">3</span>;
H = <span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>w0<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>xi<span class="org-type">/</span>w0<span class="org-type">*</span>s <span class="org-type">+</span> s<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>w0<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3189fd8" class="figure">
<p><img src="figs/hpf_second_order.png" alt="hpf_second_order.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Second Order High Pass Filter (<a href="./figs/hpf_second_order.png">png</a>, <a href="./figs/hpf_second_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
<div id="outline-container-org593e27b" class="outline-3">
<h3 id="org593e27b"><span class="section-number-3">2.3</span> Combine multiple filters</h3>
<div class="outline-text-3" id="text-2-3">
<p>
\[ H(s) = \left( \frac{s/\omega_0}{1 + s/\omega_0} \right)^n \]
</p>
<div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
n = <span class="org-highlight-numbers-number">3</span>;
H = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span>n;
</pre>
</div>
<div id="org496a810" class="figure">
<p><img src="figs/hpf_multiple_first_order.png" alt="hpf_multiple_first_order.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Combine Multiple First Order High Pass Filter (<a href="./figs/hpf_multiple_first_order.png">png</a>, <a href="./figs/hpf_multiple_first_order.pdf">pdf</a>.</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org499bdf6" class="outline-2">
<h2 id="org499bdf6"><span class="section-number-2">3</span> Band Pass</h2>
</div>
<div id="outline-container-orge29baf7" class="outline-2">
<h2 id="orge29baf7"><span class="section-number-2">4</span> Notch</h2>
</div>
<div id="outline-container-org55acbde" class="outline-2">
<h2 id="org55acbde"><span class="section-number-2">5</span> Chebyshev</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org04af1b5" class="outline-3">
<h3 id="org04af1b5"><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 = <span class="org-highlight-numbers-number">4</span>; <span class="org-comment">% Order of the filter</span>
Rp = <span class="org-highlight-numbers-number">3</span>; <span class="org-comment">% Maximum peak-to-peak ripple [dB]</span>
Wp = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% passband-edge frequency [rad/s]</span>
<span class="org-rainbow-delimiters-depth-1">[</span>A,B,C,D<span class="org-rainbow-delimiters-depth-1">]</span> = cheby1<span class="org-rainbow-delimiters-depth-1">(</span>n, Rp, Wp, <span class="org-string">'high', 's'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
H = ss<span class="org-rainbow-delimiters-depth-1">(</span>A, B, C, D<span class="org-rainbow-delimiters-depth-1">)</span>;
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<div id="orgad8bf8c" class="figure">
<p><img src="figs/cheby1_hpf.png" alt="cheby1_hpf.png" />
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<p><span class="figure-number">Figure 7: </span>First Order Low Pass Filter (<a href="./figs/cheby1_hpf.png">png</a>, <a href="./figs/cheby1_hpf.pdf">pdf</a>.</p>
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<div id="outline-container-org214e83b" class="outline-2">
<h2 id="org214e83b"><span class="section-number-2">6</span> Complementary</h2>
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-08-15 jeu. 12:24</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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