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<H1><A NAME="SECTION00890000000000000000">
Exercises</A>
</H1>
<P>
<OL>
<LI>What input to a fourth-power transfer function gives an output of -12
dB, if an input of 1 outputs 0 dB?
<P>
</LI>
<LI>An envelope generator rises from zero to a peak value during its attack
segment. How many decibels less than the peak has the output reached
halfway into the attack, assuming linear output? Fourth-power output?
<P>
</LI>
<LI>What power-law transfer function (i.e. what choice of <IMG
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ALT="$n$"> for the
function <IMG
WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img400.png"
ALT="$f(x) = {x^n}$">) would you use if you wish the halfway-point value
to be -12 decibels?
<P>
</LI>
<LI>Suppose you wish to cross-fade two signals, i.e., to ramp one signal in
and simultaneously another one out. If they have equal power and are
uncorrelated, a linear cross-fade would result in a drop of 3 decibels halfway
though the cross-fade. What power law would you use to maintain constant power
throughout the cross-fade?
<P>
</LI>
<LI>A three-note chord, lasting 1.5 seconds, is played starting once every
second. How many voices would be needed to synthesize this without cutting
off any notes?
<P>
</LI>
<LI>Suppose a synthesis patch gives output between <IMG
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SRC="img401.png"
ALT="$-1$"> and <IMG
WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img262.png"
ALT="$1$">. While
a note is playing, a new note is started using the ``rampdown" voice-stealing
technique. What is the maximum output?
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<ADDRESS>
Miller Puckette
2006-12-30
</ADDRESS>
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