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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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<TITLE>Converting from audio signals to numeric control streams</TITLE>
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<H1><A NAME="SECTION00740000000000000000">
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Converting from audio signals to numeric control streams</A>
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</H1>
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<P>
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We sometimes need to convert in the other direction, from an audio signal to a
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sporadic one. To go in this direction, we somehow provide a series of logical
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times (a time sequence), as well as an audio signal. For output we want
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a control stream combining the time sequence with values taken from the
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audio signal. We do this when we want to incorporate the signal's value as
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part of a control computation.
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<P>
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For example, we might be controlling the amplitude of a signal using a
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<TT>line~</TT> object as in Example A03.line.pd (Page
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<A HREF="node21.html#sect1.ex.3"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="crossref.png"></A>). Suppose we wish to turn off the sound at a fixed rate
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of speed instead of in a fixed amount of time. For instance, we might want to
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re-use the network for another sound and wish to mute it as quickly as possible
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without audible artifacts; we probably can ramp it off in less time if the
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current amplitude is low than if it is high. To do this we must confect a
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message to the <TT>line~</TT> object to send it to zero in an amount of
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time we'll calculate on the basis of its current output value. This will
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require, first of all, that we "sample" the <TT>line~</TT> object's
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output (an audio signal) into a control stream.
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<P>
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The same issues of time delay and accuracy appear as for sporadic to audio
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conversion. Again there will be a tradeoff between immediacy and accuracy.
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Suppose as before that we are calculating audio in blocks of 4 samples, and
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suppose that at logical time 6 we want to look at the value of an audio signal,
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and use it to change the value of another one. As shown in Figure
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<A HREF="node42.html#fig03.02">3.2</A> (part b), the most recently calculated value of the signal will
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be for index 3 and the earliest index at which our calculation can affect a
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signal is 4. We can therefore carry out the whole affair with a delay of only
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one sample. However, we can't choose exactly <I>which</I> sample--the update
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can occur only at a block boundary.
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<P>
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As before, we can trade immediacy for increased time accuracy. If it matters
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exactly at which sample we carry out the audio-to-control-to-audio computation,
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we read the sample of index 2 and update the one at index 6. Then if we want
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to do the same thing again at logical time 7, we read from index 3 and update
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at index 7, and so on. In general, if the block size is <IMG
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ALT="$B$">, and for any
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index <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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ALT="$n$">, we can always read the sample at index <IMG
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WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img329.png"
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ALT="$n-B$"> and affect the
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one at index <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img75.png"
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ALT="$n$">. There is thus a round-trip delay of <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img311.png"
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ALT="$B$"> samples in going
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from audio to control to audio computation, which is the price incurred for
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being able to name the index <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img75.png"
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ALT="$n$"> exactly.
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<P>
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If we wish to go further, to being able to specify a fraction of a sample, then
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(as before) we can use interpolation--at a slight further increase in delay.
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In general, as in the case of sporadic-to-audio conversion, in most cases the
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simplest solution is the best, but occasionally we have to do extra work.
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2006-12-30
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