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<h2>
<span class="refentrytitle">GEN14</span>
</h2>
<p>GEN14 —
Stores a polynomial whose coefficients derive from Chebyshevs of the second kind.
</p>
</div>
<div class="refsect1" title="Description">
<a id="idp77632000"></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>
</div>
<div class="refsect1" title="Syntax">
<a id="idp77665072"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 14 xint xamp h0 h1 h2 ...</pre>
</div>
<div class="refsect1" title="Initialization">
<a id="idp77666120"></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 therefore 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>
</div>
<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>
<div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;">
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<th align="left">Note</th>
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<p>
</p>
<div class="itemizedlist">
<ul class="itemizedlist" type="disc">
<li class="listitem">
<p>
<a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a> 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>
</li>
<li class="listitem">
<p>
<span class="emphasis"><em>GEN14</em></span> stores a polynomial whose coefficients derive from Chebyshevs of the second kind.
</p>
</li>
</ul>
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<p>
</p>
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<div class="refsect1" title="Examples">
<a id="idp77676616"></a>
<h2>Examples</h2>
<p>
Here is an example of the GEN14 opcode. It uses the file <a class="ulink" href="examples/gen14.csd" target="_top"><em class="citetitle">gen14.csd</em></a>.
</p>
<div class="example">
<a id="idp77677600"></a>
<p class="title">
<strong>Example 1050. Example of the GEN14 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 out</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 gen14.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">;after the example from The Csound Book, page 83</span>
<span class="oblock">instr</span> 1 <span class="comment">;compare results from GEN13 & GEN14</span>
iwshpfn <span class="op">=</span> p6
inrmfn <span class="op">=</span> p7
aswp <span class="opc">linseg</span> 0.01, p3<span class="op">*</span>.5, .49, p3<span class="op">*</span>.5, 0.01 <span class="comment">;index sweep function</span>
aindex <span class="opc">poscil</span> aswp, p5, 2 <span class="comment">;sound to waveshape</span>
atable <span class="opc">tablei</span> aindex, iwshpfn, 1, .5 <span class="comment">;waveshape index</span>
anrm <span class="opc">tablei</span> aswp<span class="op">*</span>2, inrmfn, 1 <span class="comment">;normalization </span>
aenv <span class="opc">linen</span> p4, .01, p3, .02 <span class="comment">;amplitude envelope</span>
asig <span class="op">=</span> (atable<span class="op">*</span>anrm)<span class="op">*</span>aenv <span class="comment">;normalize and impose envelope</span>
asig <span class="opc">dcblock2</span> asig <span class="comment">;get rid of DC</span>
<span class="opc">outs</span> asig, asig
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="stamnt">f</span> 2 0 8192 10 1 <span class="comment">;sine wave</span>
<span class="stamnt">f</span> 28 0 4097 13 1 1 1 0 .8 0 .5 0 .2 <span class="comment">;waveshaping function: GEN13 - odd harmonics</span>
<span class="stamnt">f</span> 280 0 2049 4 28 1 <span class="comment">;normalization function for f28</span>
<span class="stamnt">f</span> 29 0 4097 14 1 1 1 0 .8 0 .5 0 .2 <span class="comment">;waveshaping function: GEN14 - same harmonics</span>
<span class="stamnt">f</span> 290 0 2049 4 29 1 <span class="comment">;normalization function for f29</span>
<span class="stamnt">f</span> 30 0 4097 13 1 1 0 1 0 .6 0 .4 0 .1 <span class="comment">;waveshaping function: GEN13 - even harmonics</span>
<span class="stamnt">f</span> 301 0 2049 4 30 1 <span class="comment">;normalization function for f30</span>
<span class="stamnt">f</span> 31 0 4097 14 1 1 0 1 0 .6 0 .4 0 .1 <span class="comment">;waveshaping function: GEN13 - even harmonics</span>
<span class="stamnt">f</span> 310 0 2049 4 31 1 <span class="comment">;normalization function for 31</span>
<span class="stamnt">s</span>
<span class="stamnt">i</span>1 0 3 .7 440 28 280
<span class="stamnt">i</span>1 4 . .7 . 29 290
<span class="stamnt">i</span>1 8 . .7 . 30 301
<span class="stamnt">i</span>1 12 3 .7 . 31 310
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
<span>These are the diagrams of the waveforms of the GEN14 routines, as used in the example:</span>
</p>
<div class="mediaobject">
<img src="images/gen14_1.png" alt="f28 0 4097 13 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN13, odd harmonics" />
<div class="caption">
<p>f28 0 4097 13 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN13, odd harmonics</p>
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<p>
</p>
<div class="mediaobject">
<img src="images/gen14_2.png" alt="f29 0 4097 14 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN14, the same odd harmonics" />
<div class="caption">
<p>f29 0 4097 14 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN14, the same odd harmonics</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen14_3.png" alt="f30 0 4097 13 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN13, even harmonics" />
<div class="caption">
<p>f30 0 4097 13 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN13, even harmonics</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen14_4.png" alt="f31 0 4097 14 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN14, the same even harmonics" />
<div class="caption">
<p>f31 0 4097 14 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN14, the same even harmonics</p>
</div>
</div>
<p>
</p>
</div>
<div class="refsect1" title="See Also">
<a id="idp77687496"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN03.html" title="GEN03"><em class="citetitle">GEN03</em></a>,
<a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a>, and
<a class="link" href="GEN15.html" title="GEN15"><em class="citetitle">GEN15</em></a>.
</p>
<p> Information about the Chebyshev polynomials on Wikipedia: <a class="ulink" href="http://en.wikipedia.org/wiki/Chebyshev_polynomials" target="_top"><em class="citetitle">http://en.wikipedia.org/wiki/Chebyshev_polynomials</em></a></p>
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