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<refentry id="resonr">
<indexterm id="IndexResonr"><primary>resonr</primary></indexterm>
<refentryinfo><title>Signal Modifiers:Standard Filters:Resonant</title></refentryinfo>
<refmeta>
<refentrytitle>resonr</refentrytitle>
</refmeta>
<refnamediv>
<refname>resonr</refname>
<refpurpose>
A bandpass filter with variable frequency response.
</refpurpose>
</refnamediv>
<refsect1>
<title>Description</title>
<para>
Implementations of a second-order, two-pole two-zero bandpass filter with variable frequency response.
</para>
</refsect1>
<refsect1>
<title>Syntax</title>
<synopsis>ares <command>resonr</command> asig, xcf, xbw [, iscl] [, iskip]</synopsis>
</refsect1>
<refsect1>
<title>Initialization</title>
<para>
The optional initialization variables for <emphasis>resonr</emphasis> are identical to the i-time variables for <link linkend="reson"><citetitle>reson</citetitle></link>.
</para>
<para>
<emphasis>iscl</emphasis> (optional, default=0) -- coded scaling factor for resonators. A value of 1 signifies a peak response factor of 1, i.e. all frequencies other than <emphasis>kcf</emphasis> 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 <link linkend="balance"><citetitle>balance</citetitle></link>). The default value is 0.
</para>
<para>
<emphasis>iskip</emphasis> (optional, default=0) -- 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.
</para>
</refsect1>
<refsect1>
<title>Performance</title>
<para>
<emphasis>asig</emphasis> -- input signal to be filtered
</para>
<para>
<emphasis>xcf</emphasis> -- cutoff or resonant frequency of the filter, measured in Hz
</para>
<para>
<emphasis>xbw</emphasis> -- bandwidth of the filter (the Hz difference between the upper and lower half-power points)
</para>
<para>
<emphasis>resonr</emphasis> and <emphasis>resonz</emphasis> are variations of the classic two-pole bandpass resonator (<link linkend="reson"><citetitle>reson</citetitle></link>). Both filters have two zeroes in their transfer functions, in addition to the two poles. <emphasis>resonz</emphasis> has its zeroes located at z = 1 and z = -1. <emphasis>resonr</emphasis> has its zeroes located at +sqrt(<emphasis>R</emphasis>) and -sqrt(<emphasis>R</emphasis>), where <emphasis>R</emphasis> is the radius of the poles in the complex z-plane. The addition of zeroes to <emphasis>resonr</emphasis> and <emphasis>resonz</emphasis> 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.
</para>
<para>
<emphasis>resonr</emphasis> and <emphasis>resonz</emphasis> 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 <emphasis>reson</emphasis>.
</para>
<para>
<emphasis>resonr</emphasis> and <emphasis>resonz</emphasis> produce a sound that is considerably different from <emphasis>reson</emphasis>, especially for lower center frequencies; trial and error is the best way of determining which resonator is best suited for a particular application.
</para>
</refsect1>
<refsect1>
<title>Examples</title>
<para>
Here is an example of the resonr and resonz opcodes. It uses the file <ulink url="examples/resonr.csd"><citetitle>resonr.csd</citetitle></ulink>.
<example>
<title>Example of the resonr and resonz opcodes.</title>
<para>See the sections <link linkend="UsingRealTime"><citetitle>Real-time Audio</citetitle></link> and <link linkend="CommandFlags"><citetitle>Command Line Flags</citetitle></link> for more information on using command line flags.</para>
<xi:include href="examples-xml/resonr.csd.xml" xmlns:xi="http://www.w3.org/2001/XInclude"/>
</example>
</para>
</refsect1>
<refsect1>
<title>Technical History</title>
<para>
<emphasis>resonr</emphasis> and <emphasis>resonz</emphasis> were originally described in an article by Julius O. Smith and James B. Angell.<superscript>1</superscript> Smith and Angell recommended the <emphasis>resonz</emphasis> form (zeros at +1 and -1) when computational efficiency was the main concern, as it has one less multiply per sample, while <emphasis>resonr</emphasis> (zeroes at + and - the square root of the pole radius R) was recommended for situations when a perfectly constant-gain center peak was required.
</para>
<para>
Ken Steiglitz, in a later article <superscript>2</superscript>, demonstrated that <emphasis>resonz</emphasis> had constant gain at the true peak of the filter, as opposed to <emphasis>resonr</emphasis>, which displayed constant gain at the pole angle. Steiglitz also recommended <emphasis>resonz</emphasis> for its sharper notches in the gain curve at zero and Nyquist frequency. Steiglitz's recent book <superscript>3</superscript> features a thorough technical discussion of <emphasis>reson</emphasis> and <emphasis>resonz</emphasis>, while Dodge and Jerse's textbook <superscript>4</superscript> illustrates the differences in the response curves of <emphasis>reson</emphasis> and <emphasis>resonz</emphasis>.
</para>
</refsect1>
<refsect1>
<title>References</title>
<para>
<orderedlist>
<listitem>
<para>
Smith, Julius O. and Angell, James B., "A Constant-Gain Resonator Tuned by a Single Coefficient," <emphasis>Computer Music Journal</emphasis>, vol. 6, no. 4, pp. 36-39, Winter 1982.
</para>
</listitem>
<listitem>
<para>
Steiglitz, Ken, "A Note on Constant-Gain Digital Resonators," <emphasis>Computer Music Journal</emphasis>, vol. 18, no. 4, pp. 8-10, Winter 1994.
</para>
</listitem>
<listitem>
<para>
Ken Steiglitz, <emphasis>A Digital Signal Processing Primer, with Applications to Digital Audio and Computer Music</emphasis>. Addison-Wesley Publishing Company, Menlo Park, CA, 1996.
</para>
</listitem>
<listitem>
<para>
Dodge, Charles and Jerse, Thomas A., <emphasis>Computer Music: Synthesis, Composition, and Performance</emphasis>. New York: Schirmer Books, 1997, 2nd edition, pp. 211-214.
</para>
</listitem>
</orderedlist>
</para>
</refsect1>
<refsect1>
<title>See Also</title>
<para>
<link linkend="resonz"><citetitle>resonz</citetitle></link>
</para>
</refsect1>
<refsect1>
<title>Credits</title>
<para>
<simplelist>
<member>Author: &namesean;</member>
<member>Seattle, Washington</member>
<member>1999</member>
</simplelist>
</para>
<para>New in Csound version 3.55</para>
<para>Audio rate parameters introduced in version 6.02</para>
<para>November 2013.</para>
</refsect1>
</refentry>
|
