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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" title="Description">
<a id="idp77135768"></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" title="Syntax">
<a id="idp77136680"></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" title="Initialization">
<a id="idp77123504"></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>
<div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;">
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<p>
</p>
<div class="itemizedlist">
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<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" title="Examples">
<a id="idp77181360"></a>
<h2>Examples</h2>
<p>
Here is an example of the GEN03 opcode. 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="idp77182344"></a>
<p class="title">
<strong>Example 1039. Example of the GEN03 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 gen03.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">;example by Russell Pinkston - Univ. of Texas (but slightly modified)</span>
gisine <span class="ohdr">ftgen</span> 1, 0, 16384, 10, 1 <span class="comment">;sine wave</span>
<span class="oblock">instr</span> 1
ihertz <span class="op">=</span> <span class="opc">cpspch</span>(p4)
ipkamp <span class="op">=</span> p5
iwsfn <span class="op">=</span> p6 <span class="comment">;waveshaping function</span>
inmfn <span class="op">=</span> p7 <span class="comment">;normalization function</span>
aenv <span class="opc">linen</span> 1, .01, p3, .1 <span class="comment">;overall amp envelope</span>
actrl <span class="opc">linen</span> 1, 2, p3, 2 <span class="comment">;waveshaping index control</span>
aindex <span class="opc">poscil</span> actrl<span class="op">/</span>2, ihertz, gisine <span class="comment">;sine wave to be distorted</span>
asignal <span class="opc">tablei</span> .5<span class="op">+</span>aindex, iwsfn, 1 <span class="comment">;waveshaping</span>
anormal <span class="opc">tablei</span> actrl, inmfn,1 <span class="comment">;amplitude normalization</span>
asig <span class="op">=</span> asignal<span class="op">*</span>anormal<span class="op">*</span>ipkamp<span class="op">*</span>aenv
asig <span class="opc">dcblock2</span> asig <span class="comment">;get rid of possible 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="comment">; first four notes are specific Chebyshev polynomials using gen03. The values were obtained from Dodge page 147</span>
<span class="stamnt">f</span>4 0 513 3 -1 1 0 1 <span class="comment">; First-order Chebyshev: x</span>
<span class="stamnt">f</span>5 0 257 4 4 1 <span class="comment">; Normalizing function for fn4</span>
<span class="stamnt">f</span>6 0 513 3 -1 1 -1 0 2 <span class="comment">; Second-order Chebyshev: 2x2 - 1</span>
<span class="stamnt">f</span>7 0 257 4 6 1 <span class="comment">; Normalizing function for fn6</span>
<span class="stamnt">f</span>8 0 513 3 -1 1 0 -3 0 4 <span class="comment">; Third-order Chebyshev: 4x3 - 3x</span>
<span class="stamnt">f</span>9 0 257 4 8 1 <span class="comment">; Normalizing function for fn8</span>
<span class="stamnt">f</span>10 0 513 3 -1 10 0 -7 0 56 0 -112 0 64 <span class="comment">; Seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x</span>
<span class="stamnt">f</span>11 0 257 4 10 1 <span class="comment">; Normalizing function for fn10</span>
<span class="stamnt">f</span>12 0 513 3 -1 1 5 4 3 2 2 1 <span class="comment">; a 4th order polynomial function over the x-interval -1 to 1</span>
<span class="stamnt">f</span>13 0 257 4 12 1 <span class="comment">; Normalizing function for fn12</span>
<span class="comment">; five notes with same fundamental, different waveshape & normalizing functions</span>
<span class="comment">; pch amp wsfn nmfn</span>
<span class="stamnt">i</span>1 0 3 8.00 .7 4 5
<span class="stamnt">i</span>1 + . . . 6 7
<span class="stamnt">i</span>1 + . . . 8 9
<span class="stamnt">i</span>1 + . . . 10 11
<span class="stamnt">i</span>1 + . . . 12 13
<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 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" title="See Also">
<a id="idp77193832"></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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