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<H2><A NAME="SECTION0011106000000000000000">
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Non-recirculating comb filter as octave doubler</A>
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</H2>
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<P>
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In example G06.octave.doubler.pd (Figure <A HREF="#fig07.29">7.29</A>) we revisit the idea of pitch-based
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octave shifting introduced earlier in E03.octave.divider.pd. There, knowing the
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periodicity of an incoming sound allowed us to tune a ring modulator to
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introduce subharmonics. Here we realize the octave doubler described in
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Section <A HREF="node108.html#sect7.network">7.3</A>.
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Using a variable, non-recirculating comb filter we
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take out odd harmonics, leaving only the even ones, which
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sound an octave higher. As before, the spectral envelope of the sound is
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roughly preserved by the operation, so we can avoid the ``chipmunk" effect we
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would have got by using speed change to do the transposition.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.29"></A><A NAME="8278"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.29:</STRONG>
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An ``octave doubler" uses pitch information (obtained using
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a <TT>fiddle~</TT> object) to tune a comb filter to remove the odd harmonics
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in an incoming sound.</CAPTION>
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<TR><TD><IMG
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WIDTH="465" HEIGHT="376" BORDER="0"
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SRC="img838.png"
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ALT="\begin{figure}\psfig{file=figs/fig07.29.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 comb filtering is done by combining two delayed copies of the incoming
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signal (from the <TT>pd looper</TT> subpatch at top). The fixed one
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(<TT>delread~</TT>) is set to the window size of the pitch
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following algorithm. Whereas in the earlier example this was hidden in another
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subpatch, we can now show this explicitly. The delay in milliseconds is
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estimated as equal to the 2048-sample analysis window used by the
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<TT>fiddle~</TT> object; in milliseconds this comes to <!-- MATH
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$1000\cdot2048/R$
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-->
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<IMG
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WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img839.png"
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ALT="$1000\cdot2048/R$"> where
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<IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img36.png"
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ALT="$R$"> is the sample rate.
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<P>
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The variable delay is the same, plus 1/2 of the measured period of the incoming
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sound, or <IMG
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WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img840.png"
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ALT="$1000/(2f)$"> milliseconds where <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img112.png"
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ALT="$f$"> is the frequency in cycles per
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second. The sum of this and the fixed delay time is then smoothed using a
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<TT>line~</TT> object to make the input signal for the variable delay line.
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<P>
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Since the difference between the two delays is <IMG
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WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img841.png"
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ALT="$1/(2f)$">, the resonant
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frequencies of the resulting comb filter are <!-- MATH
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$2f, 4f, 6f\cdots$
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-->
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<IMG
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WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img842.png"
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ALT="$2f, 4f, 6f\cdots$">; the frequency
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response (Section <A HREF="node108.html#sect7.network">7.3</A>) is zero at the frequencies <IMG
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WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img843.png"
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ALT="$f, 3f, \ldots$">,
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so the resulting sound contains only the partials at multiples of <IMG
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WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img844.png"
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ALT="$2f$">--an
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octave above the original. Seen another way, the incoming sound is output
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twice, a half-cycle apart; odd harmonics are thereby shifted 180 degrees
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(<IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img41.png"
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ALT="$\pi $"> radians) and cancel; even harmonics are in phase with their delayed
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copies and remain in the sum.
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<P>
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Both this and the octave divider may be altered to make shifts of 3 or 4
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to one in frequency, and they may also be combined to make compound shifts
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such as a musical fifth (a ratio of 3:2) by shifting down an octave and then
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back up a factor of three. (You should do the down-shifting before the
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up-shifting for best results.)
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HREF="node116.html">Examples</A>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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