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<h2>
<span class="refentrytitle">phaser1</span>
</h2>
<p>phaser1 —
First-order allpass filters arranged in a series.
</p>
</div>
<div class="refsect1">
<a id="idm281472904065960"></a>
<h2>Description</h2>
<p>
An implementation of <span class="emphasis"><em>iord</em></span> number of first-order allpass filters in series.
</p>
</div>
<div class="refsect1">
<a id="idm281472904024120"></a>
<h2>Syntax</h2>
<pre class="synopsis">ares <span class="command"><strong>phaser1</strong></span> asig, kfreq, kord, kfeedback [, iskip]</pre>
</div>
<div class="refsect1">
<a id="idm281472904021864"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>iskip</em></span> (optional, default=0) -- used to control 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="idm281472904019544"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>kfreq</em></span> -- frequency (in Hz) of the filter(s). This is the frequency at which each filter in the series shifts its input by 90 degrees.
</p>
<p>
<span class="emphasis"><em>kord</em></span> -- the number of allpass stages in series. These are first-order filters and can range from 1 to 4999.
</p>
<div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
<table border="0" summary="Note: Note">
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<td rowspan="2" align="center" valign="top" width="25">
<img alt="[Note]" src="images/note.png" />
</td>
<th align="left">Note</th>
</tr>
<tr>
<td align="left" valign="top">
<p>
Although <span class="emphasis"><em>kord</em></span> is listed as k-rate, it is in fact accessed only at init-time. So if you are using a k-rate argument, it must be assigned with <a class="link" href="init.html" title="init"><em class="citetitle">init</em></a>.
</p>
</td>
</tr>
</table>
</div>
<p>
<span class="emphasis"><em>kfeedback</em></span> -- amount of the output which is fed back into the input of the allpass chain. With larger amounts of feedback, more prominent notches appear in the spectrum of the output. <span class="emphasis"><em>kfeedback</em></span> must be between -1 and +1. for stability.
</p>
<p>
<span class="emphasis"><em>phaser1</em></span> implements <span class="emphasis"><em>iord</em></span> number of first-order allpass sections, serially connected, all sharing the same coefficient. Each allpass section can be represented by the following difference equation:
</p>
<div class="literallayout">
<p><br />
y(n) = C * x(n) + x(n-1) - C * y(n-1)<br />
</p>
</div>
<p>
where x(n) is the input, x(n-1) is the previous input, y(n) is the output, y(n-1) is the previous output, and C is a coefficient which is calculated from the value of <span class="emphasis"><em>kfreq</em></span>, using the bilinear z-transform.
</p>
<p>
By slowly varying <span class="emphasis"><em>kfreq</em></span>, and mixing the output of the allpass chain with the input, the classic "phase shifter" effect is created, with notches moving up and down in frequency. This works best with <span class="emphasis"><em>iord</em></span> between 4 and 16. When the input to the allpass chain is mixed with the output, 1 notch is generated for every 2 allpass stages, so that with <span class="emphasis"><em>iord</em></span> = 6, there will be 3 notches in the output. With higher values for <span class="emphasis"><em>iord</em></span>, modulating <span class="emphasis"><em>kfreq</em></span> will result in a form of nonlinear pitch modulation.
</p>
</div>
<div class="refsect1">
<a id="idm281472904005480"></a>
<h2>Examples</h2>
<p>
Here is an example of the phaser1 opcode. It uses the file <a class="ulink" href="examples/phaser1.csd" target="_top"><em class="citetitle">phaser1.csd</em></a>.
</p>
<div class="example">
<a id="idm281472904003624"></a>
<p class="title">
<strong>Example 687. Example of the phaser1 opcode.</strong>
</p>
<div class="example-contents">
<p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
<div class="refsect1">
<a id="idm281472725702296"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
<span class="c1">; Select audio/midi flags here according to platform</span>
<span class="c1">; Audio out Audio in No messages</span>
-odac -iadc -d <span class="c1">;;;RT audio I/O</span>
<span class="c1">; For Non-realtime ouput leave only the line below:</span>
<span class="c1">; -o phaser1.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="vg">sr</span> <span class="o">=</span> <span class="mi">44100</span>
<span class="vg">kr</span> <span class="o">=</span> <span class="mi">4410</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">10</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1">; demonstration of phase shifting abilities of phaser1.</span>
<span class="kd">instr</span> <span class="nf">1</span>
<span class="c1">; Input mixed with output of phaser1 to generate notches.</span>
<span class="c1">; Shows the effects of different iorder values on the sound</span>
i<span class="n">dur</span> <span class="o">=</span> <span class="nb">p3</span>
i<span class="n">amp</span> <span class="o">=</span> <span class="nb">p4</span> <span class="o">*</span> <span class="mf">.05</span>
i<span class="n">order</span> <span class="o">=</span> <span class="nb">p5</span> <span class="c1">; number of 1st-order stages in phaser1 network.</span>
<span class="c1">; Divide iorder by 2 to get the number of notches.</span>
i<span class="n">freq</span> <span class="o">=</span> <span class="nb">p6</span> <span class="c1">; frequency of modulation of phaser1</span>
i<span class="n">feed</span> <span class="o">=</span> <span class="nb">p7</span> <span class="c1">; amount of feedback for phaser1</span>
k<span class="n">amp</span> <span class="nb">linseg</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">.2</span><span class="p">,</span> i<span class="n">amp</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">-</span> <span class="mf">.2</span><span class="p">,</span> i<span class="n">amp</span><span class="p">,</span> <span class="mf">.2</span><span class="p">,</span> <span class="mi">0</span>
i<span class="n">harms</span> <span class="o">=</span> <span class="p">(</span><span class="vg">sr</span><span class="o">*</span><span class="mf">.4</span><span class="p">)</span> <span class="o">/</span> <span class="mi">100</span>
a<span class="n">sig</span> <span class="nb">gbuzz</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> i<span class="n">harms</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">.95</span><span class="p">,</span> <span class="mi">2</span> <span class="c1">; "Sawtooth" waveform modulation oscillator for phaser1 ugen.</span>
k<span class="n">freq</span> <span class="nb">oscili</span> <span class="mi">5500</span><span class="p">,</span> i<span class="n">freq</span><span class="p">,</span> <span class="mi">1</span>
k<span class="n">mod</span> <span class="o">=</span> k<span class="n">freq</span> <span class="o">+</span> <span class="mi">5600</span>
a<span class="n">phs</span> <span class="nb">phaser1</span> a<span class="n">sig</span><span class="p">,</span> k<span class="n">mod</span><span class="p">,</span> i<span class="n">order</span><span class="p">,</span> i<span class="n">feed</span>
<span class="nb">out</span> <span class="p">(</span>a<span class="n">sig</span> <span class="o">+</span> a<span class="n">phs</span><span class="p">)</span> <span class="o">*</span> i<span class="n">amp</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="c1">; inverted half-sine, used for modulating phaser1 frequency</span>
<span class="nb">f</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">16384</span> <span class="mi">9</span> <span class="mf">.5</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">0</span>
<span class="c1">; cosine wave for gbuzz</span>
<span class="nb">f</span><span class="mi">2</span> <span class="mi">0</span> <span class="mi">8192</span> <span class="mi">9</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mf">.25</span>
<span class="c1">; phaser1</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">4</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">6</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">12</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">8</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">18</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">16</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">24</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">32</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">30</span> <span class="mi">5</span> <span class="mi">7000</span> <span class="mi">64</span> <span class="mf">.2</span> <span class="mf">.9</span>
<span class="nb">e</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="idm281472903999400"></a>
<h2>Technical History</h2>
<p>
A general description of the differences between flanging and phasing can be found in Hartmann [1]. An early implementation of first-order allpass filters connected in series can be found in Beigel [2], where the bilinear z-transform is used for determining the phase shift frequency of each stage. Cronin [3] presents a similar implementation for a four-stage phase shifting network. Chamberlin [4] and Smith [5] both discuss using second-order allpass sections for greater control over notch depth, width, and frequency.
</p>
</div>
<div class="refsect1">
<a id="idm281472903997128"></a>
<h2>References</h2>
<p>
</p>
<div class="orderedlist">
<ol class="orderedlist" type="1">
<li class="listitem">
<p>
Hartmann, W.M. "Flanging and Phasers." Journal of the Audio Engineering Society, Vol. 26, No. 6, pp. 439-443, June 1978.
</p>
</li>
<li class="listitem">
<p>
Beigel, Michael I. "A Digital 'Phase Shifter' for Musical Applications, Using the Bell Labs (Alles-Fischer) Digital Filter Module." Journal of the Audio Engineering Society, Vol. 27, No. 9, pp. 673-676,September 1979.
</p>
</li>
<li class="listitem">
<p>
Cronin, Dennis. "Examining Audio DSP Algorithms." Dr. Dobb's Journal, July 1994, p. 78-83.
</p>
</li>
<li class="listitem">
<p>
Chamberlin, Hal. Musical Applications of Microprocessors. Second edition. Indianapolis, Indiana: Hayden Books, 1985.
</p>
</li>
<li class="listitem">
<p>
Smith, Julius O. "An Allpass Approach to Digital Phasing and Flanging." Proceedings of the 1984 ICMC, p. 103-108.
</p>
</li>
</ol>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472903989656"></a>
<h2>See Also</h2>
<p>
<a class="link" href="phaser2.html" title="phaser2"><em class="citetitle">phaser2</em></a>
</p>
<p> Other information about phasers on Wikipedia: <a class="ulink" href="http://en.wikipedia.org/wiki/Phaser_(effect)" target="_top"><em class="citetitle">http://en.wikipedia.org/wiki/Phaser_(effect)</em></a></p>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472903986312"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Sean Costello</td>
</tr>
<tr>
<td>Seattle, Washington</td>
</tr>
<tr>
<td>1999</td>
</tr>
</table>
<p>
</p>
<p>November 2002. Added a note about the <span class="emphasis"><em>kord</em></span> parameter, thanks to Rasmus Ekman.</p>
<p>New in Csound version 4.0</p>
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