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<H1><A ID="SECTION00630000000000000000"></A>
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<A ID="sect2.enveloping"></A>
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<BR>
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Enveloping samplers
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</H1>
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<P>
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In the previous section we considered reading a wavetable either sporadically
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or repeatedly to make a sampler. In most real applications we must deal with
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getting the samples to start and stop cleanly, so that the output signal
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doesn't jump discontinuously at the beginnings and ends of samples. This
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discontinuity can sound like a click or a thump depending on the wavetable.
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<P>
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The easiest way to do this, assuming we will always play a wavetable completely
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from beginning to end, is simply to prepare it in advance so that it
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fades in cleanly at the beginning and out cleanly at the end. This may even
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be done when the wavetable is sampled live, by multiplying the
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input signal by a line segment envelope timed to match the length of the
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recording.
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<P>
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In many situations, however, it is either inconvenient or impossible to
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pre-envelope the wavetable--for example, we might want to play only part of
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it back, or we may want to change the sharpness of the enveloping
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dynamically. In Section <A HREF="node12.html#sect1.synth">1.5</A> we had already seen how
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to control the amplitude of sinusoidal oscillators using multiplication by a
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ramp function (also known as an envelope generator), and we built this notion
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into the wavetable oscillators of Figures <A HREF="node27.html#fig02.03">2.3</A> and <A HREF="node27.html#fig02.04">2.4</A>.
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This also works fine for turning samplers on and off to avoid discontinuities,
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but with one major difference: whereas in wavetable synthesis, we were free to
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assume that the waveform lines up end to end, so that we may choose
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any envelope timing we want, in the case of sampling using unprepared waveforms,
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we are obliged to get the envelope generator's output to zero by the time we
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reach the end of the wavetable for the first time. This situation is pictured
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in Figure <A HREF="#fig02.06">2.6</A>.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig02.06"></A><A ID="2243"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2.6:</STRONG>
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Differing envelope requirements for oscillators and samplers: (a)
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in an oscillator, the envelope can be chosen to conform to any desired
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timescale; (b) when the wavetable is a recorded sound, it's up to you
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to get the envelope to zero before you hit the end of the wavetable for the
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first time. </CAPTION>
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<TR><TD><IMG
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WIDTH="453" HEIGHT="278" BORDER="0"
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SRC="img218.png"
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ALT="\begin{figure}\psfig{file=figs/fig02.06.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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In situations where an arbitrary wavetable must be repeated as needed, the
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simplest way to make the looping work continuously is to arrange for amplitude
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change to be synchronized with the looping, using a separate wavetable (the
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envelope). This may be implemented as shown in Figure <A HREF="#fig02.07">2.7</A>. A single
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sawtooth oscillator is used to calculate lookup indices for two wavetables, one
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holding the recorded sound, and the other, an envelope shape. The main thing
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to worry about is getting the inputs of the two wavetables each into its own
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appropriate range.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig02.07"></A><A ID="2500"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2.7:</STRONG>
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A sampler as in Figure <A HREF="node28.html#fig02.05">2.5</A>, but with an additional
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wavetable lookup for enveloping.</CAPTION>
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<TR><TD><IMG
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WIDTH="325" HEIGHT="440" BORDER="0"
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SRC="img219.png"
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ALT="\begin{figure}\psfig{file=figs/fig02.07.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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In many situations it is desirable to combine two or more copies of the looping
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wavetable sampler at the same frequency and at a specified phase relationship.
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This may be done so that when any particular one is at the end of its segment,
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one or more others is in the middle of the same segment, so that the aggregate
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is continuously making sound. To accomplish this, we need a way to generate
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two or more sawtooth waves at the desired phase relationship that we can use in
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place of the oscillator at the top of Figure <A HREF="#fig02.07">2.7</A>. We can start with
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a single sawtooth wave and then produce others at fixed phase relationships
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with the first one. If we wish a sawtooth which is, say, <IMG
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WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$a$"> cycles ahead of
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the first one, we simply add the parameter <IMG
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WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$a$"> and then take the fractional
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part, which is the desired new sawtooth wave, as shown in Figure <A HREF="#fig02.08">2.8</A>.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig02.08"></A><A ID="2256"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2.8:</STRONG>
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A technique for generating two or more sawtooth waves with
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fixed phase relationships between
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them. The relative phase is controlled by the parameter <IMG
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WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$a$"> (which takes the
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value 0.3 in the graphed signals). The "wrap" operation computes the fractional
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part of its input.</CAPTION>
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<TR><TD><IMG
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WIDTH="603" HEIGHT="402" BORDER="0"
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SRC="img220.png"
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ALT="\begin{figure}\psfig{file=figs/fig02.08.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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HREF="node26.html">Wavetables and samplers</A>
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HREF="node28.html">Sampling</A>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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