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<h2>
<span class="refentrytitle">zdf_ladder</span>
</h2>
<p>zdf_ladder —
Zero-delay feedback implementation of 4 pole ladder filter.
</p>
</div>
<div class="refsect1">
<a id="idm281472866853192"></a>
<h2>Description</h2>
<p>
Zero-delay feedback implementation of a 4 pole (24 dB/oct) low-pass filter based on the Moog ladder filter.
</p>
</div>
<div class="refsect1">
<a id="idm281472866849592"></a>
<h2>Syntax</h2>
<pre class="synopsis">asig <span class="command"><strong>zdf_ladder</strong></span> ain, xcf, xQ [, istor]</pre>
</div>
<div class="refsect1">
<a id="idm281472866847384"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>istor</em></span> --initial disposition of internal data space.
Since filtering incorporates a feedback loop of previous output, the
initial status of the storage space used is significant. A zero value
will clear the space; a non-zero value will allow previous information to
remain. The default value is 0.
</p>
</div>
<div class="refsect1">
<a id="idm281472866783176"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>asig</em></span> -- output signal.
</p>
<p>
<span class="emphasis"><em>asig</em></span> -- input signal.
</p>
<p>
<span class="emphasis"><em>xcf</em></span> -- filter cutoff frequency (i-, k-, or a-rate).
</p>
<p>
<span class="emphasis"><em>xQ</em></span> -- filter Q value (i-, k-, or a-rate). Range 0.5-25.0. Self-oscillation occurs at 25.0.
</p>
</div>
<div class="refsect1">
<a id="idm281472866779128"></a>
<h2>Examples</h2>
<p>
Here is an example of the zdf_ladder opcode. It uses the file <a class="ulink" href="examples/zdf_ladder.csd" target="_top"><em class="citetitle">zdf_ladder.csd</em></a>.
</p>
<div class="example">
<a id="idm281472866777352"></a>
<p class="title">
<strong>Example 1156. Example of the zdf_ladder opcode.</strong>
</p>
<div class="example-contents">
<div class="refsect1">
<a id="idm281472685384968"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
-o dac
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="vg">sr</span> <span class="o">=</span> <span class="mi">48000</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">1</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">2</span>
<span class="vg">0dbfs</span> <span class="o">=</span> <span class="mi">1</span>
<span class="kd">instr</span> <span class="nf">1</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="nb">random</span><span class="p">:</span><span class="nb">a</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">)</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="n">zdf_ladder</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> <span class="nb">expon</span><span class="p">(</span><span class="mi">220</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="mi">5000</span><span class="p">),</span> <span class="nb">p4</span><span class="p">)</span>
<span class="nb">outc</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> a<span class="n">sig</span><span class="p">)</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">2</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="nb">vco2</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">220</span><span class="p">)</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="n">zdf_ladder</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> <span class="nb">expon</span><span class="p">(</span><span class="mi">220</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="mi">5000</span><span class="p">),</span> <span class="nb">p4</span><span class="p">)</span>
<span class="nb">outc</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> a<span class="n">sig</span><span class="p">)</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">3</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="nb">vco2</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="nb">p4</span><span class="p">)</span>
a<span class="n">sig</span> <span class="o">=</span> <span class="n">zdf_ladder</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> <span class="nb">expon</span><span class="p">(</span><span class="mi">5000</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="mi">200</span><span class="p">),</span> <span class="mf">0.5</span> <span class="o">+</span> <span class="nb">p5</span><span class="o">*</span> <span class="mi">24</span><span class="p">)</span>
a<span class="n">sig</span> <span class="o">*=</span> <span class="nb">madsr</span><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">)</span>
<span class="nb">outc</span><span class="p">(</span>a<span class="n">sig</span><span class="p">,</span> a<span class="n">sig</span><span class="p">)</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">play_instr3</span>
<span class="nb">schedule</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="nb">mtof</span><span class="p">(</span><span class="mi">48</span> <span class="o">+</span> <span class="p">(</span><span class="nb">p4</span> <span class="o">%</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="mi">12</span><span class="p">),</span> <span class="nb">p4</span> <span class="o">/</span> <span class="mi">16</span><span class="p">)</span>
<span class="k">if</span><span class="p">(</span><span class="nb">p4</span> <span class="o"><</span> <span class="mi">16</span><span class="p">)</span> <span class="k">then</span>
<span class="nb">schedule</span><span class="p">(</span><span class="s">"play_instr3"</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="nb">p4</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">else</span>
<span class="nb">event_i</span><span class="p">(</span><span class="s">"e"</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="k">endif</span>
<span class="nb">turnoff</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">2</span> <span class="mf">0.5</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">1</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">4</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">10</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">18</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="mf">24.5</span>
<span class="nb">i</span><span class="mi">2</span> <span class="mi">12</span> <span class="mi">2</span> <span class="mf">0.5</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">1</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">4</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">10</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="o">.</span> <span class="mi">18</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="o">.</span> <span class="mf">24.5</span>
<span class="nb">s</span>
<span class="nb">i</span> <span class="s">"play_instr3"</span> <span class="mi">0</span> <span class="mf">0.25</span> <span class="mi">0</span>
<span class="nb">f</span><span class="mi">0</span> <span class="mi">60</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
</div>
</div>
</div>
<p><br class="example-break" />
</p>
</div>
<div class="refsect1">
<a id="idm281472866775432"></a>
<h2>References</h2>
<p> This filter is based on the work of Will Pirkle that employs Vadim
Zavalishin's work with bilinear tranforms to create topology-preserving
transform (TPT) implementations of analog filters.</p>
<p>
</p>
<div class="orderedlist">
<ol class="orderedlist" type="1">
<li class="listitem">
<p>
Pirkle, Will. Designing Software Synthesizer Plug-ins in C++: For
RackAFX, VST3, and Audio Units. CRC Press, 2014.
</p>
</li>
<li class="listitem">
<p>
Pirkle, Will. AN-4: Virtual Analog (VA) Filter Implementation. 2013.
</p>
</li>
<li class="listitem">
<p>
Zavalishin, Vadim. "The Art of VA filter design." Native Instruments, 2012.
</p>
</li>
</ol>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472866769992"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Steven Yi</td>
</tr>
<tr>
<td>April 2017</td>
</tr>
</table>
<p>
</p>
<p>New in Csound 6.09.0</p>
</div>
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