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HREF="node61.html">Continuous and discontinuous control</A>
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HREF="node62.html">Muting</A>
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<H2><A ID="SECTION00832000000000000000">
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Switch-and-ramp</A>
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</H2>
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<P>
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The
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<A ID="4648"></A>
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<I>switch-and-ramp</I>
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technique also seeks to remove discontinuities resulting from discontinuous
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control changes, but does so in a different way: by synthesizing an opposing
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discontinuity which we add to cancel the original one out. Figure
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<A HREF="#fig04.06">4.6</A> shows an example in which a synthetic percussive sound (an
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enveloped sinusoid) starts a note in the middle of a previous one. The attack
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of the sound derives not from the amplitude envelope but from the initial phase
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of the sinusoid, as is often appropriate for percussive sounds. The lower
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graph in the figure shows a compensating audio signal with an opposing
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discontinuity, which can be added to the upper one to remove the discontinuity.
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The advantages of this technique over muting are, first, that there need be no
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delay between the decision to make an attack and the sound of the attack; and
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second, that any artifacts arising from this technique are more likely to be
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masked by the new sound's onset.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig04.06"></A><A ID="4653"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4.6:</STRONG>
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The switch-and-ramp technique for canceling out discontinuous changes.
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A discontinuity (upper graph) is measured and canceled out with a signal
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having the opposite discontinuity (lower graph), which then decays smoothly.</CAPTION>
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<TR><TD><IMG
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WIDTH="298" HEIGHT="121" BORDER="0"
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SRC="img369.png"
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ALT="\begin{figure}\psfig{file=figs/fig04.06.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="#fig04.07">4.7</A> shows how the switch-and-ramp technique can be realized
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in a block diagram. The box marked with ellipsis ("...") may hold any
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synthesis algorithm, which we wish to interrupt discontinuously so that it
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restarts from zero (as in, for example, part (a) of the previous figure). At
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the same time that we trigger whatever control changes are necessary (exemplified by
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the top ADSR generator), we also reset and trigger another ADSR generator
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(middle right) to cancel out the discontinuity. The discontinuity is minus the
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last value of the synthesis output just before it is reset to zero.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig04.07"></A><A ID="4659"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4.7:</STRONG>
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Block diagram for the switch-and-ramp technique.</CAPTION>
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<TR><TD><IMG
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WIDTH="256" HEIGHT="373" BORDER="0"
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SRC="img370.png"
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ALT="\begin{figure}\psfig{file=figs/fig04.07.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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To do this we measure the level the ADSR generator must now jump to. This is
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its own current level (which might not be zero) minus the discontinuity (or
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equivalently, <I>plus</I> the synthesis output's last value). The two are
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added (by the <TT>+~</TT> object at bottom), and then a snapshot is taken.
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The cancelling envelope generator (at right) is reset discontinuously to this
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new value, and then triggered to ramp back to zero. The <TT>+~</TT> object's
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output (the sum of the synthesizer output and the discontinuity-cancelling
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signal) is the de-clicked signal.
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HREF="node64.html">Polyphony</A>
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<B> Up:</B> <A ID="tex2html1482"
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HREF="node61.html">Continuous and discontinuous control</A>
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<B> Previous:</B> <A ID="tex2html1478"
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HREF="node62.html">Muting</A>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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