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<div class="refentry" title="polynomial">
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<h2>
<span class="refentrytitle">polynomial</span>
</h2>
<p>polynomial —
Efficiently evaluates a polynomial of arbitrary order.
</p>
</div>
<div class="refsect1" title="Description">
<a id="idp36719016"></a>
<h2>Description</h2>
<p>
The <span class="emphasis"><em>polynomial</em></span> opcode calculates a polynomial with a single a-rate input variable. The polynomial is a sum of any number of terms in the form <span class="emphasis"><em>kn*x^n</em></span> where <span class="emphasis"><em>kn</em></span> is the nth coefficient of the expression. These coefficients are k-rate values.
</p>
</div>
<div class="refsect1" title="Syntax">
<a id="idp36720464"></a>
<h2>Syntax</h2>
<pre class="synopsis">aout <span class="command"><strong>polynomial</strong></span> ain, k0 [, k1 [, k2 [...]]]</pre>
</div>
<div class="refsect1" title="Performance">
<a id="idp36721576"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>ain</em></span> -- the input signal used as the independent variable of the polynomial ("x").
</p>
<p>
<span class="emphasis"><em>aout</em></span> -- the output signal ("y").
</p>
<p>
<span class="emphasis"><em>k0, k1, k2, ...</em></span> -- the coefficients for each term of the polynomial.
</p>
<p>
If we consider the input parameter <span class="emphasis"><em>ain</em></span> to be "x" and the output <span class="emphasis"><em>aout</em></span> to be "y", then the <span class="emphasis"><em>polynomial</em></span> opcode calculates the following equation:
</p>
<div class="literallayout">
<p><br />
y = k0 + k1*x + k2*x^2 + k3*x^3 + ...<br />
</p>
</div>
<p>
</p>
</div>
<div class="refsect1" title="Examples">
<a id="idp36724872"></a>
<h2>Examples</h2>
<p>
Here is an example of the polynomial opcode. It uses the file <a class="ulink" href="examples/polynomial.csd" target="_top"><em class="citetitle">polynomial.csd</em></a>.
</p>
<div class="example">
<a id="idp36725864"></a>
<p class="title">
<strong>Example 602. Example of the polynomial 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>
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
-odac <span class="comment">;;;realtime audio</span>
<span class="comment">;-iadc ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o polynomial.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">ksmps</span> <span class="op">=</span> 32
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="ohdr">0dbfs</span> <span class="op">=</span> 1
<span class="comment">; The polynomial y=x^n where n is odd always produces a curve</span>
<span class="comment">; that traverses the range [-1, 1] when the input is within</span>
<span class="comment">; the same range. Therefore, we can use one of these curves</span>
<span class="comment">; to make a nonlinear phasor that repeatedly reads a table </span>
<span class="comment">; from beginning to end like a linear phasor (maintaining </span>
<span class="comment">; continuity) but that distorts the waveform in the table.</span>
<span class="oblock">instr</span> 4 <span class="comment">; This instrument demonstrates phase distortion with x^3</span>
idur <span class="op">=</span> p3
iamp <span class="op">=</span> p4
ifreq <span class="op">=</span> p5
itable <span class="op">=</span> p6
aenv <span class="opc">linseg</span> 0, .001, 1.0, idur <span class="op">-</span> .051, 1.0, .05, 0 <span class="comment">; declicking envelope</span>
aosc <span class="opc">phasor</span> ifreq <span class="comment">; create a linear phasor</span>
apd <span class="opc">polynomial</span> aosc, 0, 0, 0, 1 <span class="comment">; distort the phasor with x^3</span>
aout <span class="opc">tablei</span> apd, itable, 1 <span class="comment">; read a sine table with the nonlinear phasor</span>
<span class="opc">outs</span> aenv<span class="op">*</span>aout<span class="op">*</span>iamp, aenv<span class="op">*</span>aout<span class="op">*</span>iamp
<span class="oblock">endin</span>
<span class="oblock">instr</span> 5 <span class="comment">; This instrument demonstrates phase distortion with x^11</span>
idur <span class="op">=</span> p3
iamp <span class="op">=</span> p4
ifreq <span class="op">=</span> p5
itable <span class="op">=</span> p6
aenv <span class="opc">linseg</span> 0, .001, 1.0, idur <span class="op">-</span> .051, 1.0, .05, 0 <span class="comment">; declicking envelope</span>
aosc <span class="opc">phasor</span> ifreq <span class="comment">; create a linear phasor</span>
apd <span class="opc">polynomial</span> aosc, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 <span class="comment">; distort the phasor with x^11</span>
aout <span class="opc">tablei</span> apd, itable, 1 <span class="comment">; read a sine table with the nonlinear phasor</span>
<span class="opc">outs</span> aenv<span class="op">*</span>aout<span class="op">*</span>iamp, aenv<span class="op">*</span>aout<span class="op">*</span>iamp
<span class="oblock">endin</span>
<span class="oblock">instr</span> 6 <span class="comment">; This instrument crossfades between a pure sine and one distorted with x^11</span>
idur <span class="op">=</span> p3
iamp <span class="op">=</span> p4
ifreq <span class="op">=</span> p5
itable <span class="op">=</span> p6
aenv <span class="opc">linseg</span> 0, .001, 1.0, idur <span class="op">-</span> .051, 1.0, .05, 0 <span class="comment">; declicking envelope</span>
aosc <span class="opc">phasor</span> ifreq <span class="comment">; create a linear phasor</span>
aout3 <span class="opc">tablei</span> aosc, itable, 1 <span class="comment">; read a sine table without the linear phasor</span>
apd11 <span class="opc">polynomial</span> aosc, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 <span class="comment">; distort the phasor with x^11</span>
aout11 <span class="opc">tablei</span> apd11, itable, 1 <span class="comment">; read a sine table with the nonlinear phasor</span>
kamount <span class="opc">linseg</span> 1.0, 0.05, 0.9, 1.0, 0.0 <span class="comment">; crossfade between two outputs</span>
aout <span class="op">=</span> aout3<span class="op">*</span>kamount <span class="op">+</span> aout11<span class="op">*</span>(1.0 <span class="op">-</span> kamount)
<span class="opc">outs</span> aenv<span class="op">*</span>aout<span class="op">*</span>iamp, aenv<span class="op">*</span>aout<span class="op">*</span>iamp
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="stamnt">f</span>1 0 16385 10 1 <span class="comment">; sine wave</span>
<span class="comment">; descending "just blues" scale</span>
<span class="stamnt">t</span> 0 100
<span class="stamnt">i</span>4 0 .333 .7 512 1
<span class="stamnt">i</span>. + . . 448
<span class="stamnt">i</span>. + . . 384
<span class="stamnt">i</span>. + . . 360
<span class="stamnt">i</span>. + . . 341.33
<span class="stamnt">i</span>. + . . 298.67
<span class="stamnt">i</span>. + 2 . 256
<span class="stamnt">s</span>
<span class="stamnt">t</span> 0 100
<span class="stamnt">i</span>5 0 .333 .7 512 1
<span class="stamnt">i</span>. + . . 448
<span class="stamnt">i</span>. + . . 384
<span class="stamnt">i</span>. + . . 360
<span class="stamnt">i</span>. + . . 341.33
<span class="stamnt">i</span>. + . . 298.67
<span class="stamnt">i</span>. + 2 . 256
<span class="stamnt">s</span>
<span class="stamnt">t</span> 0 100
<span class="stamnt">i</span>6 0 .333 .7 512 1
<span class="stamnt">i</span>. + . . 448
<span class="stamnt">i</span>. + . . 384
<span class="stamnt">i</span>. + . . 360
<span class="stamnt">i</span>. + . . 341.33
<span class="stamnt">i</span>. + . . 298.67
<span class="stamnt">i</span>. + 2 . 256
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
</p>
</div>
<div class="refsect1" title="See Also">
<a id="idp36728144"></a>
<h2>See Also</h2>
<p>
<a class="link" href="chebyshevpoly.html" title="chebyshevpoly"><em class="citetitle">chebyshevpoly</em></a>,
<a class="link" href="mac.html" title="mac"><em class="citetitle">mac</em></a>
<a class="link" href="maca.html" title="maca"><em class="citetitle">maca</em></a>
</p>
</div>
<div class="refsect1" title="Credits">
<a id="idp36730096"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Anthony Kozar</td>
</tr>
<tr>
<td>January 2008</td>
</tr>
</table>
<p>
</p>
<p>New in Csound version 5.08</p>
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