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<h2>
<span class="refentrytitle">GEN03</span>
</h2>
<p>GEN03 —
Generates a stored function table by evaluating a polynomial.
</p>
</div>
<div class="refsect1">
<a id="idm281472820634024"></a>
<h2>Description</h2>
<p>
This subroutine generates a stored function table by evaluating a polynomial in x over a fixed interval and with specified coefficients.
</p>
</div>
<div class="refsect1">
<a id="idm281472820552872"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 3 xval1 xval2 c0 c1 c2 ... cn</pre>
</div>
<div class="refsect1">
<a id="idm281472820550824"></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.
</p>
<p>
<span class="emphasis"><em>xval1, xval2 </em></span> -- left and right values of the x interval over which the polynomial is defined (<span class="emphasis"><em>xval1</em></span> < <span class="emphasis"><em>xval2</em></span>). These will produce the 1st stored value and the (power-of-2 plus l)th stored value respectively in the generated function table.
</p>
<p>
<span class="emphasis"><em>c0, c1, c2, ..., cn</em></span> -- coefficients of the nth-order polynomial
</p>
<p>
<span class="emphasis"><em>C<sub>0</sub></em></span> + <span class="emphasis"><em>C<sub>1</sub>x</em></span> +
<span class="emphasis"><em>C<sub>2</sub>x<sup>2</sup></em></span> + . . . +
<span class="emphasis"><em>C<sub>n</sub>x<sup>n</sup></em></span>
</p>
<p>
Coefficients may be positive or negative real numbers; a zero denotes a missing term in the polynomial. The coefficient list begins in p7, providing a current upper limit of 144 terms.
</p>
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<th align="left">Note</th>
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<p>
</p>
<div class="itemizedlist">
<ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p>
The defined segment [fn(<span class="emphasis"><em>xval1</em></span>), fn(<span class="emphasis"><em>xval2</em></span>)] is evenly distributed. Thus a 512-point table over the interval [-1,1] will have its origin at location 257 (at the start of the 2nd half). Provided the extended guard point is requested, both fn(-1) and fn(1) will exist in the table.
</p>
</li>
<li class="listitem">
<p>
<span class="emphasis"><em>GEN03</em></span> is useful in conjunction with <a class="link" href="table.html" title="table"><em class="citetitle">table</em></a> or <a class="link" href="tablei.html" title="tablei"><em class="citetitle">tablei</em></a> for audio waveshaping (sound modification by non-linear distortion). Coefficients to produce a particular formant from a sinusoidal lookup index of known amplitude can be determined at preprocessing time using algorithms such as Chebyshev formulae. See also <a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a>.
</p>
</li>
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<div class="refsect1">
<a id="idm281472820533096"></a>
<h2>Examples</h2>
<p>
Here is an example of the GEN03 generator. It uses the file <a class="ulink" href="examples/gen03.csd" target="_top"><em class="citetitle">gen03.csd</em></a>.
</p>
<div class="example">
<a id="idm281472820531304"></a>
<p class="title">
<strong>Example 1184. Example of the GEN03 generator.</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>
<div class="refsect1">
<a id="idm281472683279544"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
<span class="c1">; Select audio/midi flags here according to platform</span>
-odac <span class="c1">;;;realtime audio out</span>
<span class="c1">;-iadc ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="c1">; For Non-realtime ouput leave only the line below:</span>
<span class="c1">; -o gen03.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="vg">sr</span> <span class="o">=</span> <span class="mi">44100</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">32</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">2</span>
<span class="vg">0dbfs</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1">;example by Russell Pinkston - Univ. of Texas (but slightly modified)</span>
gi<span class="n">sine</span> <span class="nb">ftgen</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">16384</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">;sine wave</span>
<span class="kd">instr</span> <span class="nf">1</span>
i<span class="n">hertz</span> <span class="o">=</span> <span class="nb">cpspch</span><span class="p">(</span><span class="nb">p4</span><span class="p">)</span>
i<span class="n">pkamp</span> <span class="o">=</span> <span class="nb">p5</span>
i<span class="n">wsfn</span> <span class="o">=</span> <span class="nb">p6</span> <span class="c1">;waveshaping function</span>
i<span class="n">nmfn</span> <span class="o">=</span> <span class="nb">p7</span> <span class="c1">;normalization function</span>
a<span class="n">env</span> <span class="nb">linen</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">.01</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="mf">.1</span> <span class="c1">;overall amp envelope</span>
a<span class="n">ctrl</span> <span class="nb">linen</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="mi">2</span> <span class="c1">;waveshaping index control</span>
a<span class="n">index</span> <span class="nb">poscil</span> a<span class="n">ctrl</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> i<span class="n">hertz</span><span class="p">,</span> gi<span class="n">sine</span> <span class="c1">;sine wave to be distorted</span>
a<span class="n">signal</span> <span class="nb">tablei</span> <span class="mf">.5</span><span class="o">+</span>a<span class="n">index</span><span class="p">,</span> i<span class="n">wsfn</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">;waveshaping</span>
a<span class="n">normal</span> <span class="nb">tablei</span> a<span class="n">ctrl</span><span class="p">,</span> i<span class="n">nmfn</span><span class="p">,</span><span class="mi">1</span> <span class="c1">;amplitude normalization</span>
a<span class="n">sig</span> <span class="o">=</span> a<span class="n">signal</span><span class="o">*</span>a<span class="n">normal</span><span class="o">*</span>i<span class="n">pkamp</span><span class="o">*</span>a<span class="n">env</span>
a<span class="n">sig</span> <span class="nb">dcblock2</span> a<span class="n">sig</span> <span class="c1">;get rid of possible DC </span>
<span class="nb">outs</span> a<span class="n">sig</span><span class="p">,</span> a<span class="n">sig</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="c1">; first four notes are specific Chebyshev polynomials using gen03. The values were obtained from Dodge page 147</span>
<span class="nb">f</span><span class="mi">4</span> <span class="mi">0</span> <span class="mi">513</span> <span class="mi">3</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">1</span> <span class="c1">; First-order Chebyshev: x</span>
<span class="nb">f</span><span class="mi">5</span> <span class="mi">0</span> <span class="mi">257</span> <span class="mi">4</span> <span class="mi">4</span> <span class="mi">1</span> <span class="c1">; Normalizing function for fn4</span>
<span class="nb">f</span><span class="mi">6</span> <span class="mi">0</span> <span class="mi">513</span> <span class="mi">3</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">1</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">2</span> <span class="c1">; Second-order Chebyshev: 2x2 - 1</span>
<span class="nb">f</span><span class="mi">7</span> <span class="mi">0</span> <span class="mi">257</span> <span class="mi">4</span> <span class="mi">6</span> <span class="mi">1</span> <span class="c1">; Normalizing function for fn6</span>
<span class="nb">f</span><span class="mi">8</span> <span class="mi">0</span> <span class="mi">513</span> <span class="mi">3</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="o">-</span><span class="mi">3</span> <span class="mi">0</span> <span class="mi">4</span> <span class="c1">; Third-order Chebyshev: 4x3 - 3x</span>
<span class="nb">f</span><span class="mi">9</span> <span class="mi">0</span> <span class="mi">257</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">1</span> <span class="c1">; Normalizing function for fn8</span>
<span class="nb">f</span><span class="mi">10</span> <span class="mi">0</span> <span class="mi">513</span> <span class="mi">3</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">10</span> <span class="mi">0</span> <span class="o">-</span><span class="mi">7</span> <span class="mi">0</span> <span class="mi">56</span> <span class="mi">0</span> <span class="o">-</span><span class="mi">112</span> <span class="mi">0</span> <span class="mi">64</span> <span class="c1">; Seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x</span>
<span class="nb">f</span><span class="mi">11</span> <span class="mi">0</span> <span class="mi">257</span> <span class="mi">4</span> <span class="mi">10</span> <span class="mi">1</span> <span class="c1">; Normalizing function for fn10</span>
<span class="nb">f</span><span class="mi">12</span> <span class="mi">0</span> <span class="mi">513</span> <span class="mi">3</span> <span class="o">-</span><span class="mi">1</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">2</span> <span class="mi">1</span> <span class="c1">; a 4th order polynomial function over the x-interval -1 to 1</span>
<span class="nb">f</span><span class="mi">13</span> <span class="mi">0</span> <span class="mi">257</span> <span class="mi">4</span> <span class="mi">12</span> <span class="mi">1</span> <span class="c1">; Normalizing function for fn12</span>
<span class="c1">; five notes with same fundamental, different waveshape & normalizing functions</span>
<span class="c1">; pch amp wsfn nmfn</span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">3</span> <span class="mf">8.00</span> <span class="mf">.7</span> <span class="mi">4</span> <span class="mi">5</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">6</span> <span class="mi">7</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">8</span> <span class="mi">9</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">10</span> <span class="mi">11</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">12</span> <span class="mi">13</span>
<span class="nb">e</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
</div>
</div>
</div>
<p><br class="example-break" />
<span class="phrase">These are the diagrams of the waveforms of the GEN03 routines, as used in the example:</span>
</p>
<div class="mediaobject">
<img src="images/gen03_1.png" alt="f4 0 513 3 1 1 0 1 - first-order Chebyshev: x" />
<div class="caption">
<p>f4 0 513 3 1 1 0 1 - first-order Chebyshev: x</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen03_2.png" alt="f6 0 513 3 -1 1 -1 0 2 - second-order Chebyshev: 2x2 - 1" />
<div class="caption">
<p>f6 0 513 3 -1 1 -1 0 2 - second-order Chebyshev: 2x2 - 1</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen03_3.png" alt="f8 0 513 3 -1 1 0 -3 0 4 - third-order Chebyshev: 4x3 - 3x" />
<div class="caption">
<p>f8 0 513 3 -1 1 0 -3 0 4 - third-order Chebyshev: 4x3 - 3x</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen03_4.png" alt="f10 0 513 3 -1 10 0 -7 0 56 0 -112 0 64 - seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x" />
<div class="caption">
<p>f10 0 513 3 -1 10 0 -7 0 56 0 -112 0 64 - seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen03_5.png" alt="f12 0 513 3 -1 1 5 4 3 2 2 1 - a 4th order polynomial function over the x-interval -1 to 1" />
<div class="caption">
<p>f12 0 513 3 -1 1 5 4 3 2 2 1 - a 4th order polynomial function over the x-interval -1 to 1</p>
</div>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472820509384"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</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>.
</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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