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<refentry id="phaser1">
<indexterm id="IndexPhaser1"><primary>phaser1</primary></indexterm>
<refentryinfo><title>Signal Modifiers:Special Effects</title></refentryinfo>
<refmeta>
<refentrytitle>phaser1</refentrytitle>
</refmeta>
<refnamediv>
<refname>phaser1</refname>
<refpurpose>
First-order allpass filters arranged in a series.
</refpurpose>
</refnamediv>
<refsect1>
<title>Description</title>
<para>
An implementation of <emphasis>iord</emphasis> number of first-order allpass filters in series.
</para>
</refsect1>
<refsect1>
<title>Syntax</title>
<synopsis>ares <command>phaser1</command> asig, kfreq, kord, kfeedback [, iskip]</synopsis>
</refsect1>
<refsect1>
<title>Initialization</title>
<para>
<emphasis>iskip</emphasis> (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.
</para>
</refsect1>
<refsect1>
<title>Performance</title>
<para>
<emphasis>kfreq</emphasis> -- frequency (in Hz) of the filter(s). This is the frequency at which each filter in the series shifts its input by 90 degrees.
</para>
<para>
<emphasis>kord</emphasis> -- the number of allpass stages in series. These are first-order filters and can range from 1 to 4999.
</para>
<note>
<title>Note</title>
<para>
Although <emphasis>kord</emphasis> 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 <link linkend="init"><citetitle>init</citetitle></link>.
</para>
</note>
<para>
<emphasis>kfeedback</emphasis> -- 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. <emphasis>kfeedback</emphasis> must be between -1 and +1. for stability.
</para>
<para>
<emphasis>phaser1</emphasis> implements <emphasis>iord</emphasis> number of first-order allpass sections, serially connected, all sharing the same coefficient. Each allpass section can be represented by the following difference equation:
<literallayout>
y(n) = C * x(n) + x(n-1) - C * y(n-1)
</literallayout>
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 <emphasis>kfreq</emphasis>, using the bilinear z-transform.
</para>
<para>
By slowly varying <emphasis>kfreq</emphasis>, 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 <emphasis>iord</emphasis> 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 <emphasis>iord</emphasis> = 6, there will be 3 notches in the output. With higher values for <emphasis>iord</emphasis>, modulating <emphasis>kfreq</emphasis> will result in a form of nonlinear pitch modulation.
</para>
</refsect1>
<refsect1>
<title>Examples</title>
<para>
Here is an example of the phaser1 opcode. It uses the file <ulink url="examples/phaser1.csd"><citetitle>phaser1.csd</citetitle></ulink>.
<example>
<title>Example of the phaser1 opcode.</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/phaser1.csd.xml" xmlns:xi="http://www.w3.org/2001/XInclude"/>
</example>
</para>
</refsect1>
<refsect1>
<title>Technical History</title>
<para>
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.
</para>
</refsect1>
<refsect1>
<title>References</title>
<para>
<orderedlist>
<listitem>
<para>
Hartmann, W.M. "Flanging and Phasers." Journal of the Audio Engineering Society, Vol. 26, No. 6, pp. 439-443, June 1978.
</para>
</listitem>
<listitem>
<para>
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.
</para>
</listitem>
<listitem>
<para>
Cronin, Dennis. "Examining Audio DSP Algorithms." Dr. Dobb's Journal, July 1994, p. 78-83.
</para>
</listitem>
<listitem>
<para>
Chamberlin, Hal. Musical Applications of Microprocessors. Second edition. Indianapolis, Indiana: Hayden Books, 1985.
</para>
</listitem>
<listitem>
<para>
Smith, Julius O. "An Allpass Approach to Digital Phasing and Flanging." Proceedings of the 1984 ICMC, p. 103-108.
</para>
</listitem>
</orderedlist>
</para>
</refsect1>
<refsect1>
<title>See Also</title>
<para>
<link linkend="phaser2"><citetitle>phaser2</citetitle></link>
<para> Other information about phasers on Wikipedia: <ulink url="http://en.wikipedia.org/wiki/Phaser_(effect)"><citetitle>http://en.wikipedia.org/wiki/Phaser_(effect)</citetitle></ulink></para>
</para>
</refsect1>
<refsect1>
<title>Credits</title>
<para>
<simplelist>
<member>Author: &namesean;</member>
<member>Seattle, Washington</member>
<member>1999</member>
</simplelist>
</para>
<para>November 2002. Added a note about the <emphasis>kord</emphasis> parameter, thanks to &namerasmus;.</para>
<para>New in Csound version 4.0</para>
</refsect1>
</refentry>
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