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<TITLE>Reverberator</TITLE>
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<BR>
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<B> Next:</B> <A NAME="tex2html2404"
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HREF="node125.html">Pitch shifter</A>
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HREF="node123.html">Time-varying complex comb filter:</A>
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<H2><A NAME="SECTION0011108000000000000000">
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Reverberator</A>
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</H2>
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<P>
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Example G08.reverb.pd (Figure <A HREF="#fig07.31">7.31</A>) shows a simple artificial reverberator,
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essentially a realization of the design shown in Figure <A HREF="node111.html#fig07.15">7.15</A>. Four
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delay lines are fed by the input and by their own recirculated output. The
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delay outputs are intermixed using rotation matrices, built up from elementary
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rotations of <IMG
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WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img52.png"
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ALT="$\pi /4$"> as in Figure <A HREF="node110.html#fig07.13">7.13</A> (part a).
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.31"></A><A NAME="8301"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.31:</STRONG>
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An artificial reverberator.</CAPTION>
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<TR><TD><IMG
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WIDTH="585" HEIGHT="811" BORDER="0"
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SRC="img846.png"
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ALT="\begin{figure}\psfig{file=figs/fig07.31.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 normalizing
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multiplication (by <IMG
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SRC="img847.png"
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ALT="$\sqrt{1/2}$"> at each stage) is absorbed into the feedback
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gain, which therefore cannot exceed <IMG
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WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img98.png"
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ALT="$1/2$">.
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At a feedback gain of exactly <IMG
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WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img98.png"
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ALT="$1/2$">, all the energy leaving the delay lines is
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reinserted into them, so the reverberation lasts perpetually.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.32"></A><A NAME="8307"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.32:</STRONG>
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The echo generator used in the reverberator.</CAPTION>
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<TR><TD><IMG
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WIDTH="230" HEIGHT="164" BORDER="0"
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SRC="img848.png"
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ALT="\begin{figure}\psfig{file=figs/fig07.32.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Figure <A HREF="#fig07.32">7.32</A> shows the interior of the <TT>reverb-echo</TT> abstraction
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used in the reverberator. The two inputs are mixed (using the same rotation matrix
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and again leaving the renormalization for later). One channel is then
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delayed. The delay times are selected to grow roughly exponentially; this
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ensures a smooth and spread-out pattern of echos.
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<P>
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Many extensions of this idea are possible of which we'll only name a few. It
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is natural, first, to put low-pass filters at the end of the delay lines, to
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mimic the typically faster decay of high frequencies than low ones. It is also
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common to use more than four recirculating delays; one reverberator in the Pd
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distribution uses sixteen. Finally, it is common to allow separate control of
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the amplitudes of the early echos (heard directly) and that of the
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recirculating signal; parameters such as these are thought to control
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sonic qualities described as ``presence", ``warmth", ``clarity", and so on.
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HREF="node123.html">Time-varying complex comb filter:</A>
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<B> <A NAME="tex2html2400"
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<ADDRESS>
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Miller Puckette
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2006-12-30
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