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<h2>
<span class="refentrytitle">GEN13</span>
</h2>
<p>GEN13 —
Stores a polynomial whose coefficients derive from the Chebyshev polynomials of the first kind.
</p>
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<div class="refsect1" title="Description">
<a id="id3735308"></a>
<h2>Description</h2>
<p>
Uses Chebyshev coefficients to generate stored polynomial functions which, under waveshaping, can be used to split a sinusoid into harmonic partials having a pre-definable spectrum.
</p>
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<div class="refsect1" title="Syntax">
<a id="id3735325"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 13 xint xamp h0 h1 h2 ...</pre>
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<div class="refsect1" title="Initialization">
<a id="id3735540"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>size</em></span> -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1 (see <a class="link" href="f.html" title="f Statement (or Function Table Statement)"><em class="citetitle">f statement</em></a>). The normal value is power-of-2 plus 1.
</p>
<p>
<span class="emphasis"><em>xint</em></span> -- provides the left and right values [<span class="emphasis"><em>-xint, +xint</em></span>] of the x interval over which the polynomial is to be drawn. These subroutines both call <a class="link" href="GEN03.html" title="GEN03"><em class="citetitle">GEN03</em></a> to draw their functions; the p5 value here is therefor expanded to a negative-positive p5, p6 pair before <span class="emphasis"><em>GEN03</em></span> is actually called. The normal value is 1.
</p>
<p>
<span class="emphasis"><em>xamp </em></span> -- amplitude scaling factor of the sinusoid input that is expected to produce the following spectrum.
</p>
<p>
<span class="emphasis"><em>h0, h1, h2,</em></span> etc. -- relative strength of partials 0 (DC), 1 (fundamental), 2 ... that will result when a sinusoid of amplitude
</p>
<div class="literallayout">
<p><br />
xamp * int(size/2)/xint<br />
</p>
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<p>
is waveshaped using this function table. These values thus describe a frequency spectrum associated with a particular factor <span class="emphasis"><em>xamp</em></span> of the input signal.
</p>
<p>
<span class="emphasis"><em>GEN13</em></span> is the function generator normally employed in standard waveshaping. It stores a polynomial whose coefficients derive from the Chebyshev polynomials of the first kind, so that a driving sinusoid of strength <span class="emphasis"><em>xamp</em></span> will exhibit the specified spectrum at output. Note that the evolution of this spectrum is generally not linear with varying <span class="emphasis"><em>xamp</em></span>. However, it is bandlimited (the only partials to appear will be those specified at generation time); and the partials will tend to occur and to develop in ascending order (the lower partials dominating at low <span class="emphasis"><em>xamp</em></span>, and the spectral richness increasing for higher values of <span class="emphasis"><em>xamp</em></span>). A negative <span class="emphasis"><em>hn</em></span> value implies a 180 degree phase shift of that partial; the requested full-amplitude spectrum will not be affected by this shift, although the evolution of several of its component partials may be. The pattern +,+,-,-,+,+,... for <span class="emphasis"><em>h0,h1,h2..</em></span>. will minimize the normalization problem for low <span class="emphasis"><em>xamp</em></span> values (see above), but does not necessarily provide the smoothest pattern of evolution.
</p>
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<div class="refsect1" title="Examples">
<a id="id3736310"></a>
<h2>Examples</h2>
<p>
Here is a simple example of the GEN13 routine. It uses the file <a class="ulink" href="examples/gen13.csd" target="_top"><em class="citetitle">gen13.csd</em></a>. It creates a function which, under waveshaping, will split a sinusoid into 3 odd-harmonic partials of relative strength 5:3:1. Here is its diagram:
</p>
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<img src="images/gen13.png" alt="Diagram of the waveform generated by GEN13." />
<div class="caption">
<p>Diagram of the waveform generated by GEN13.</p>
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<p>
</p>
<div class="example">
<a id="id3736360"></a>
<p class="title">
<b>Example 745. A simple example of the GEN13 routine.</b>
</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>
<span class="comment">; Audio out Audio in</span>
-odac -iadc <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o gen13.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="comment">; Initialize the global variables.</span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 1
<span class="comment">; Instrument #1.</span>
<span class="oblock">instr</span> 1
<span class="comment">; Create an index over the length of our entire note.</span>
kcps <span class="opc">init</span> 1<span class="op">/</span>p3
kndx <span class="opc">phasor</span> kcps
<span class="comment">; Read Table #1 with our index.</span>
ifn <span class="op">=</span> 1
ixmode <span class="op">=</span> 1
kval <span class="opc">table</span> kndx, ifn, ixmode
<span class="comment">; Generate a sine waveform, use our Table #1 value to</span>
<span class="comment">; vary its frequency by 100 Hz from its base frequency.</span>
ibasefreq <span class="op">=</span> 440
kfreq <span class="op">=</span> kval <span class="op">*</span> 100
a1 <span class="opc">oscil</span> 20000, ibasefreq <span class="op">+</span> kfreq, 2
<span class="opc">out</span> a1
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="comment">; Table #1: a polynomial function (using GEN13).</span>
<span class="stamnt">f</span> 1 0 1025 13 1 1 0 5 0 3 0 1
<span class="comment">; Table #2, a sine wave.</span>
<span class="stamnt">f</span> 2 0 16384 10 1
<span class="comment">; Play Instrument #1 for 2 seconds.</span>
<span class="stamnt">i</span> 1 0 2
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
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<p><br class="example-break" />
</p>
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<div class="refsect1" title="See Also">
<a id="id3736399"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN03.html" title="GEN03"><em class="citetitle">GEN03</em></a>,
<a class="link" href="GEN14.html" title="GEN14"><em class="citetitle">GEN14</em></a>, and
<a class="link" href="GEN15.html" title="GEN15"><em class="citetitle">GEN15</em></a>.
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