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<TITLE>GEN13</TITLE>
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<H2>GEN13, GEN14</H2>
<PRE><TT> <B>f</B> # time size 13 xint xamp h0 h1 h2 . . . hn
<B>f</B> # time size 14 xint xamp h0 h1 h2 . . . hn </TT>
</PRE>
<P>
<HR></P>
<H4><U>DESCRIPTION</U></H4>
<P>These subroutines use Chebyshev coefficients to generate stored polynomial
functions which, under waveshaping, can be used to split a sinusoid into
harmonic partials having a predefinable spectrum.
<HR></P>
<H4><U>INITIALIZATION</U></H4>
<P><I>size</I> - number of points in the table. Must be a power of 2 or
a power-of-2 plus 1 ( <A HREF="./../NumScore/f-stat.html">see f statement</A>).
The normal value is power-of-2 plus 1. </P>
<P><I>xint</I> - provides the left and right values [<I>-xint, +xint</I>]
of the x interval over which the polynomial is to be drawn. These subroutines
both call <B><A HREF="./gen03.html">GEN03</A></B> to draw their functions; the
p5 value here is therefor expanded to a negative-positive p5,p6 pair before
<B><A HREF="./gen03.html">GEN03</A></B> is actually called. The normal value
is 1.</P>
<P><I>xamp </I>- amplitude scaling factor of the sinusoid input that is
expected to produce the following spectrum.</P>
<P><I>h0, h1, h2, .... hn</I> - relative strength of partials 0 (DC), 1
(fundamental), 2 ... that will result when a sinusoid of amplitude <I>xamp
* int(size/2)/xint</I> is waveshaped using this function table. These values
thus describe a frequency spectrum associated with a particular factor
<I>xamp</I> of the input signal.</P>
<P>Note: </P>
<P><B>GEN13</B> 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 <I>xamp</I> will exhibit the specified spectrum at output. Note
that the evolution of this spectrum is generally not linear with varying
<I>xamp</I>. 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
<I>xamp</I>, and the spectral richness increasing for higher values of
<I>xamp</I>). A negative <I>hn</I> 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 <I>h0,h1,h2..</I>. will minimize
the normalization problem for low <I>xamp</I> values (see above), but does
not necessarily provide the smoothest pattern of evolution. </P>
<P><B>GEN14</B> stores a polynomial whose coefficients derive from Chebyshevs
of the second kind. </P>
<H4><U>EXAMPLE:</U></H4>
<PRE><TT> f 1 0 1025 13 1 1 0 5 0 3 0 1 </TT>
</PRE>
<P>This creates a function which, under waveshaping, will split a sinusoid
into 3 odd-harmonic partials of relative strength 5:3:1. </P>
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