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<TITLE>Wavetable pulse train</TITLE>
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html2013"
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HREF="node201.html">Index</A></B>
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<H2><A ID="SECTION001051000000000000000">
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Wavetable pulse train</A>
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</H2>
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<P>
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Example F01.pulse.pd (Figure <A HREF="#fig06.12">6.13</A>) generates a variable-width pulse train
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using stretched wavetable lookup. Figure
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<A HREF="#fig06.13">6.14</A> shows two intermediate products of the patch and its output.
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The patch carries out the job in the simplest possible way, placing the
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pulse at phase <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img41.png"
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ALT="$\pi $"> instead of phase zero; in later
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examples this will be fixed by adding 0.5 to the phase and wrapping.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig06.12"></A><A ID="6962"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6.13:</STRONG>
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Example patch F01.pulse.pd, which synthesizes a pulse train using
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stretched wavetable lookup.</CAPTION>
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<TR><TD><IMG
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WIDTH="436" HEIGHT="408" BORDER="0"
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SRC="img610.png"
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ALT="\begin{figure}\psfig{file=figs/fig06.12.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<DIV ALIGN="CENTER"><A ID="fig06.13"></A><A ID="7046"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6.14:</STRONG>
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Intermediate audio signals from Figure <A HREF="#fig06.12">6.13</A>: (a) the
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result of multiplying the phasor by the "index"; (b) the same, clipped to
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lie between -0.5 and 0.5; (c) the output.</CAPTION>
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<TR><TD><IMG
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WIDTH="349" HEIGHT="429" BORDER="0"
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SRC="img611.png"
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ALT="\begin{figure}\psfig{file=figs/fig06.13.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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The initial phase is adjusted to run from -0.5 to 0.5 and then scaled by a
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multiplier of at least one, resulting in the signal of Figure <A HREF="#fig06.13">6.14</A>
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(part a); this corresponds to the output of the <TT>*~</TT> object, fifth
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from bottom in the patch shown. The graph in part (b) shows the result of
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clipping the sawtooth wave back to the interval between <IMG
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WIDTH="36" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img612.png"
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ALT="$-0.5$"> and <IMG
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WIDTH="23" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img613.png"
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ALT="$0.5$">, using the
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<TT>clip~</TT> object. If the scaling multiplier were at its minimum (one), the
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sawtooth would only range from -0.5 to 0.5 anyway and the clipping would have
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no effect. For any value of the scaling multiplier greater than one, the
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clipping output sits at the value -0.5, then ramps to 0.5, then sits at 0.5.
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The higher the multiplier, the faster the waveform ramps and the
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more time it spends clipped at the bottom and top.
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<P>
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The <TT>cos~</TT> object then converts this waveform into a pulse. Inputs of
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both -0.5 and 0.5 go to -1 (they are one cycle apart); at the midpoint of
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the waveform, the input is 0 and the output is thus 1. The output therefore
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sits at -1, traces a full cycle of the cosine function, then comes back to
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rest at -1. The proportion of time the waveform spends tracing the cosine
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function is one divided by the multiplier; so it's 100% for a multiplier
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of 1, 50% for 2, and so on.
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Finally, the pulse output is adjusted to range from 0 to 1 in
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value; this is graphed in part (c) of the figure.
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<P>
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<B> <A ID="tex2html2013"
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Miller Puckette
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