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<refentry id="filter2">
<indexterm id="IndexFilter2"><primary>filter2</primary></indexterm>
<refentryinfo><title>Signal Modifiers:Specialized Filters</title></refentryinfo>
<refmeta>
<refentrytitle>filter2</refentrytitle>
</refmeta>
<refnamediv>
<refname>filter2</refname>
<refpurpose>
Performs filtering using a transposed form-II digital filter lattice with no time-varying control.
</refpurpose>
</refnamediv>
<refsect1>
<title>Description</title>
<para>
General purpose custom filter with no time-varying pole control. The filter coefficients implement the following difference equation:
<literallayout>
(1)*y(n) = b0*x[n] + b1*x[n-1] +...+ bM*x[n-M] - a1*y[n-1] -...- aN*y[n-N]
</literallayout>
</para>
<para>
the system function for which is represented by:
<literallayout>
B(Z) b0 + b1*Z<superscript>-1</superscript> + ... + bM*Z<superscript>-M</superscript>
H(Z) = ---- = --------------------------
A(Z) 1 + a1*Z<superscript>-1</superscript> + ... + aN*Z<superscript>-N</superscript>
</literallayout>
</para>
</refsect1>
<refsect1>
<title>Syntax</title>
<synopsis>ares <command>filter2</command> asig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN</synopsis>
<synopsis>kres <command>filter2</command> ksig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN</synopsis>
</refsect1>
<refsect1>
<title>Initialization</title>
<para>
At initialization the number of zeros and poles of the filter are specified along with the corresponding zero and pole coefficients. The coefficients must be obtained by an external filter-design application such as Matlab and specified directly or loaded into a table via <link linkend="GEN01"><citetitle>GEN01</citetitle></link>.
</para>
</refsect1>
<refsect1>
<title>Performance</title>
<para>
The<emphasis> filter2</emphasis> opcodes perform filtering using a transposed form-II digital filter lattice with no time-varying control.
</para>
<para>
Since <emphasis>filter2</emphasis> implements generalized recursive filters, it can be used to specify a large range of general DSP algorithms. For example, a digital waveguide can be implemented for musical instrument modeling using a pair of <link linkend="delayr"><citetitle>delayr</citetitle></link> and <link linkend="delayw"><citetitle>delayw</citetitle></link> opcodes in conjunction with the <emphasis>filter2</emphasis> opcode.
</para>
</refsect1>
<refsect1>
<title>Examples</title>
<para>
A first-order linear-phase lowpass FIR filter operating on a k-rate signal:
<informalexample>
<programlisting>
k1 <emphasis role="opc">filter2</emphasis> ksig, 2, 0, 0.5, 0.5 <emphasis role="comment">;; k-rate FIR filter</emphasis></programlisting>
</informalexample>
</para>
<para>
Here is another example of the filter2 opcode. It uses the file <ulink url="examples/filter2.csd"><citetitle>filter2.csd</citetitle></ulink>.
<example>
<title>Example of the filter2 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/filter2.csd.xml" xmlns:xi="http://www.w3.org/2001/XInclude"/>
</example>
</para>
</refsect1>
<refsect1>
<title>See Also</title>
<para>
<link linkend="zfilter2"><citetitle>zfilter2</citetitle></link>
</para>
</refsect1>
<refsect1>
<title>Credits</title>
<para>
<simplelist>
<member>Author: Michael A. Casey</member>
<member>M.I.T.</member>
<member>Cambridge, Mass.</member>
<member>1997</member>
</simplelist>
</para>
<para>New in version 3.47</para>
</refsect1>
</refentry>
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