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<h2>
<span class="refentrytitle">resonz</span>
</h2>
<p>resonz —
A bandpass filter with variable frequency response.
</p>
</div>
<div class="refsect1">
<a id="idm281472895106840"></a>
<h2>Description</h2>
<p>
Implementations of a second-order, two-pole two-zero bandpass filter with variable frequency response.
</p>
</div>
<div class="refsect1">
<a id="idm281472895105528"></a>
<h2>Syntax</h2>
<pre class="synopsis">ares <span class="command"><strong>resonz</strong></span> asig, xcf, xbw [, iscl] [, iskip]</pre>
</div>
<div class="refsect1">
<a id="idm281472895032024"></a>
<h2>Initialization</h2>
<p>
The optional initialization variables for <span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> are identical to the i-time variables for <a class="link" href="reson.html" title="reson"><em class="citetitle">reson</em></a>.
</p>
<p>
<span class="emphasis"><em>iskip</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>
<p>
<span class="emphasis"><em>iscl</em></span> -- coded scaling factor for resonators. A value of 1 signifies a peak response factor of 1, i.e. all frequencies other than <span class="emphasis"><em>kcf</em></span> are attenuated in accordance with the (normalized) response curve. A value of 2 raises the response factor so that its overall RMS value equals 1. This intended equalization of input and output power assumes all frequencies are physically present; hence it is most applicable to white noise. A zero value signifies no scaling of the signal, leaving that to some later adjustment (see <a class="link" href="balance.html" title="balance"><em class="citetitle">balance</em></a>). The default value is 0.
</p>
</div>
<div class="refsect1">
<a id="idm281472895025064"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> are variations of the classic two-pole bandpass resonator (<a class="link" href="reson.html" title="reson"><em class="citetitle">reson</em></a>). Both filters have two zeroes in their transfer functions, in addition to the two poles. <span class="emphasis"><em>resonz</em></span> has its zeroes located at z = 1 and z = -1. <span class="emphasis"><em>resonr</em></span> has its zeroes located at +sqrt(<span class="emphasis"><em>R</em></span>) and -sqrt(<span class="emphasis"><em>R</em></span>), where <span class="emphasis"><em>R</em></span> is the radius of the poles in the complex z-plane. The addition of zeroes to <span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> results in the improved selectivity of the magnitude response of these filters at cutoff frequencies close to 0, at the expense of less selectivity of frequencies above the cutoff peak.
</p>
<p>
<span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> are very close to constant-gain as the center frequency is swept, resulting in a more efficient control of the magnitude response than with traditional two-pole resonators such as <span class="emphasis"><em>reson</em></span>.
</p>
<p>
<span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> produce a sound that is considerably different from <span class="emphasis"><em>reson</em></span>, especially for lower center frequencies; trial and error is the best way of determining which resonator is best suited for a particular application.
</p>
<p>
<span class="emphasis"><em>asig</em></span> -- input signal to be filtered
</p>
<p>
<span class="emphasis"><em>xcf</em></span> -- cutoff or resonant frequency of the filter, measured in Hz
</p>
<p>
<span class="emphasis"><em>xbw</em></span> -- bandwidth of the filter (the Hz difference between the upper and lower half-power points)
</p>
</div>
<div class="refsect1">
<a id="idm281472895012296"></a>
<h2>Technical History</h2>
<p>
<span class="emphasis"><em>resonr</em></span> and <span class="emphasis"><em>resonz</em></span> were originally described in an article by Julius O. Smith and James B. Angell.<sup>1</sup> Smith and Angell recommended the <span class="emphasis"><em>resonz</em></span> form (zeros at +1 and -1) when computational efficiency was the main concern, as it has one less multiply per sample, while <span class="emphasis"><em>resonr</em></span> (zeroes at + and - the square root of the pole radius R) was recommended for situations when a perfectly constant-gain center peak was required.
</p>
<p>
Ken Steiglitz, in a later article <sup>2</sup>, demonstrated that <span class="emphasis"><em>resonz</em></span> had constant gain at the true peak of the filter, as opposed to <span class="emphasis"><em>resonr</em></span>, which displayed constant gain at the pole angle. Steiglitz also recommended <span class="emphasis"><em>resonz</em></span> for its sharper notches in the gain curve at zero and Nyquist frequency. Steiglitz's recent book <sup>3</sup> features a thorough technical discussion of <span class="emphasis"><em>reson</em></span> and <span class="emphasis"><em>resonz</em></span>, while Dodge and Jerse's textbook <sup>4</sup> illustrates the differences in the response curves of <span class="emphasis"><em>reson</em></span> and <span class="emphasis"><em>resonz</em></span>.
</p>
</div>
<div class="refsect1">
<a id="idm281472895003480"></a>
<h2>Examples</h2>
<p>
Here is an example of the resonr and resonz opcodes. It uses the file <a class="ulink" href="examples/resonr.csd" target="_top"><em class="citetitle">resonr.csd</em></a>.
</p>
<div class="example">
<a id="idm281472895001608"></a>
<p class="title">
<strong>Example 828. Example of the resonr and resonz opcodes.</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="idm281472716109160"></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 resonr.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="cm">/* Written by Sean Costello */</span>
<span class="c1">; Orchestra file for resonant filter sweep of a sawtooth-like waveform. </span>
<span class="c1">; The outputs of reson, resonr, and resonz are scaled by coefficients</span>
<span class="c1">; specified in the score, so that each filter can be heard on its own</span>
<span class="c1">; from the same instrument.</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="kd">instr</span> <span class="nf">1</span>
i<span class="n">dur</span> <span class="o">=</span> <span class="nb">p3</span>
i<span class="n">begfreq</span> <span class="o">=</span> <span class="nb">p4</span> <span class="c1">; beginning of sweep frequency</span>
i<span class="n">endfreq</span> <span class="o">=</span> <span class="nb">p5</span> <span class="c1">; ending of sweep frequency</span>
i<span class="n">bw</span> <span class="o">=</span> <span class="nb">p6</span> <span class="c1">; bandwidth of filters in Hz</span>
i<span class="n">freq</span> <span class="o">=</span> <span class="nb">p7</span> <span class="c1">; frequency of gbuzz that is to be filtered</span>
i<span class="n">amp</span> <span class="o">=</span> <span class="nb">p8</span> <span class="c1">; amplitude to scale output by</span>
i<span class="n">res</span> <span class="o">=</span> <span class="nb">p9</span> <span class="c1">; coefficient to scale amount of reson in output</span>
i<span class="n">resr</span> <span class="o">=</span> <span class="nb">p10</span> <span class="c1">; coefficient to scale amount of resonr in output</span>
i<span class="n">resz</span> <span class="o">=</span> <span class="nb">p11</span> <span class="c1">; coefficient to scale amount of resonz in output</span>
<span class="c1">; Frequency envelope for reson cutoff</span>
k<span class="n">freq</span> <span class="nb">linseg</span> i<span class="n">begfreq</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">*</span> <span class="mf">.5</span><span class="p">,</span> i<span class="n">endfreq</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">*</span> <span class="mf">.5</span><span class="p">,</span> i<span class="n">begfreq</span>
<span class="c1">; Amplitude envelope to prevent clicking</span>
k<span class="n">env</span> <span class="nb">linseg</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">.1</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">.1</span><span class="p">,</span> <span class="mi">0</span>
<span class="c1">; Number of harmonics for gbuzz scaled to avoid aliasing</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>i<span class="n">freq</span>
a<span class="n">sig</span> <span class="nb">gbuzz</span> <span class="mi">1</span><span class="p">,</span> i<span class="n">freq</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">.9</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; "Sawtooth" waveform</span>
a<span class="n">in</span> <span class="o">=</span> k<span class="n">env</span> <span class="o">*</span> a<span class="n">sig</span> <span class="c1">; output scaled by amp envelope</span>
a<span class="n">res</span> <span class="nb">reson</span> a<span class="n">in</span><span class="p">,</span> k<span class="n">freq</span><span class="p">,</span> i<span class="n">bw</span><span class="p">,</span> <span class="mi">1</span>
a<span class="n">resr</span> <span class="nb">resonr</span> a<span class="n">in</span><span class="p">,</span> k<span class="n">freq</span><span class="p">,</span> i<span class="n">bw</span><span class="p">,</span> <span class="mi">1</span>
a<span class="n">resz</span> <span class="nb">resonz</span> a<span class="n">in</span><span class="p">,</span> k<span class="n">freq</span><span class="p">,</span> i<span class="n">bw</span><span class="p">,</span> <span class="mi">1</span>
<span class="nb">out</span> a<span class="n">res</span> <span class="o">*</span> i<span class="n">res</span> <span class="o">+</span> a<span class="n">resr</span> <span class="o">*</span> i<span class="n">resr</span> <span class="o">+</span> a<span class="n">resz</span> <span class="o">*</span> i<span class="n">resz</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="cm">/* Written by Sean Costello */</span>
<span class="nb">f</span><span class="mi">1</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">; cosine table for gbuzz generator</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">200</span> <span class="mi">100</span> <span class="mi">4000</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span> <span class="c1">; reson output with bw = 200</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">10</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">200</span> <span class="mi">100</span> <span class="mi">4000</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">0</span> <span class="c1">; resonr output with bw = 200</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">20</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">200</span> <span class="mi">100</span> <span class="mi">4000</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="c1">; resonz output with bw = 200</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">30</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">50</span> <span class="mi">200</span> <span class="mi">8000</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span> <span class="c1">; reson output with bw = 50</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">40</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">50</span> <span class="mi">200</span> <span class="mi">8000</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">0</span> <span class="c1">; resonr output with bw = 50</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">50</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">3000</span> <span class="mi">50</span> <span class="mi">200</span> <span class="mi">8000</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="c1">; resonz output with bw = 50</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="idm281472894997304"></a>
<h2>References</h2>
<p>
</p>
<div class="orderedlist">
<ol class="orderedlist" type="1">
<li class="listitem">
<p>
Smith, Julius O. and Angell, James B., "A Constant-Gain Resonator Tuned by a Single Coefficient," <span class="emphasis"><em>Computer Music Journal</em></span>, vol. 6, no. 4, pp. 36-39, Winter 1982.
</p>
</li>
<li class="listitem">
<p>
Steiglitz, Ken, "A Note on Constant-Gain Digital Resonators," <span class="emphasis"><em>Computer Music Journal</em></span>, vol. 18, no. 4, pp. 8-10, Winter 1994.
</p>
</li>
<li class="listitem">
<p>
Ken Steiglitz, <span class="emphasis"><em>A Digital Signal Processing Primer, with Applications to Digital Audio and Computer Music</em></span>. Addison-Wesley Publishing Company, Menlo Park, CA, 1996.
</p>
</li>
<li class="listitem">
<p>
Dodge, Charles and Jerse, Thomas A., <span class="emphasis"><em>Computer Music: Synthesis, Composition, and Performance</em></span>. New York: Schirmer Books, 1997, 2nd edition, pp. 211-214.
</p>
</li>
</ol>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472894989448"></a>
<h2>See Also</h2>
<p>
<a class="link" href="resonr.html" title="resonr"><em class="citetitle">resonr</em></a>
</p>
</div>
<div class="refsect1">
<a id="idm281472894987336"></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>New in Csound version 3.55</p>
<p>Audio rate parameters introduced in version 6.02</p>
<p>November 2013.</p>
</div>
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