You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
205 lines
7.0 KiB
205 lines
7.0 KiB
<!DOCTYPE html>
|
|
|
|
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
* with significant contributions from:
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
<HTML>
|
|
<HEAD>
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
<TITLE>Non-recirculating comb filter as octave doubler</TITLE>
|
|
<META NAME="description" CONTENT="Non-recirculating comb filter as octave doubler">
|
|
<META NAME="keywords" CONTENT="book">
|
|
<META NAME="resource-type" CONTENT="document">
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="book.css">
|
|
|
|
<LINK REL="next" HREF="node123.html">
|
|
<LINK REL="previous" HREF="node121.html">
|
|
<LINK REL="up" HREF="node116.html">
|
|
<LINK REL="next" HREF="node123.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2375"
|
|
HREF="node123.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2369"
|
|
HREF="node116.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2363"
|
|
HREF="node121.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2371"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2373"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2376"
|
|
HREF="node123.html">Time-varying complex comb filter:</A>
|
|
<B> Up:</B> <A ID="tex2html2370"
|
|
HREF="node116.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html2364"
|
|
HREF="node121.html">Order of execution in</A>
|
|
<B> <A ID="tex2html2372"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2374"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A ID="SECTION0011106000000000000000">
|
|
Non-recirculating comb filter as octave doubler</A>
|
|
</H2>
|
|
|
|
<P>
|
|
In example G06.octave.doubler.pd (Figure <A HREF="#fig07.29">7.29</A>) we revisit the idea of pitch-based
|
|
octave shifting introduced earlier in E03.octave.divider.pd. There, knowing the
|
|
periodicity of an incoming sound allowed us to tune a ring modulator to
|
|
introduce subharmonics. Here we realize the octave doubler described in
|
|
Section <A HREF="node108.html#sect7.network">7.3</A>.
|
|
Using a variable, non-recirculating comb filter we
|
|
take out odd harmonics, leaving only the even ones, which
|
|
sound an octave higher. As before, the spectral envelope of the sound is
|
|
roughly preserved by the operation, so we can avoid the "chipmunk" effect we
|
|
would have got by using speed change to do the transposition.
|
|
|
|
<P>
|
|
|
|
<DIV ALIGN="CENTER"><A ID="fig07.29"></A><A ID="8278"></A>
|
|
<TABLE>
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.29:</STRONG>
|
|
An "octave doubler" uses pitch information (obtained using
|
|
a <TT>fiddle~</TT> object) to tune a comb filter to remove the odd harmonics
|
|
in an incoming sound.</CAPTION>
|
|
<TR><TD><IMG
|
|
WIDTH="465" HEIGHT="376" BORDER="0"
|
|
SRC="img838.png"
|
|
ALT="\begin{figure}\psfig{file=figs/fig07.29.ps}\end{figure}"></TD></TR>
|
|
</TABLE>
|
|
</DIV>
|
|
|
|
<P>
|
|
The comb filtering is done by combining two delayed copies of the incoming
|
|
signal (from the <TT>pd looper</TT> subpatch at top). The fixed one
|
|
(<TT>delread~</TT>) is set to the window size of the pitch
|
|
following algorithm. Whereas in the earlier example this was hidden in another
|
|
subpatch, we can now show this explicitly. The delay in milliseconds is
|
|
estimated as equal to the 2048-sample analysis window used by the
|
|
<TT>fiddle~</TT> object; in milliseconds this comes to <!-- MATH
|
|
$1000\cdot2048/R$
|
|
-->
|
|
<IMG
|
|
WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img839.png"
|
|
ALT="$1000\cdot2048/R$"> where
|
|
<IMG
|
|
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img36.png"
|
|
ALT="$R$"> is the sample rate.
|
|
|
|
<P>
|
|
The variable delay is the same, plus 1/2 of the measured period of the incoming
|
|
sound, or <IMG
|
|
WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img840.png"
|
|
ALT="$1000/(2f)$"> milliseconds where <IMG
|
|
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img112.png"
|
|
ALT="$f$"> is the frequency in cycles per
|
|
second. The sum of this and the fixed delay time is then smoothed using a
|
|
<TT>line~</TT> object to make the input signal for the variable delay line.
|
|
|
|
<P>
|
|
Since the difference between the two delays is <IMG
|
|
WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img841.png"
|
|
ALT="$1/(2f)$">, the resonant
|
|
frequencies of the resulting comb filter are <!-- MATH
|
|
$2f, 4f, 6f\cdots$
|
|
-->
|
|
<IMG
|
|
WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img842.png"
|
|
ALT="$2f, 4f, 6f\cdots$">; the frequency
|
|
response (Section <A HREF="node108.html#sect7.network">7.3</A>) is zero at the frequencies <IMG
|
|
WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img843.png"
|
|
ALT="$f, 3f, \ldots$">,
|
|
so the resulting sound contains only the partials at multiples of <IMG
|
|
WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img844.png"
|
|
ALT="$2f$">--an
|
|
octave above the original. Seen another way, the incoming sound is output
|
|
twice, a half-cycle apart; odd harmonics are thereby shifted 180 degrees
|
|
(<IMG
|
|
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img41.png"
|
|
ALT="$\pi $"> radians) and cancel; even harmonics are in phase with their delayed
|
|
copies and remain in the sum.
|
|
|
|
<P>
|
|
Both this and the octave divider may be altered to make shifts of 3 or 4
|
|
to one in frequency, and they may also be combined to make compound shifts
|
|
such as a musical fifth (a ratio of 3:2) by shifting down an octave and then
|
|
back up a factor of three. (You should do the down-shifting before the
|
|
up-shifting for best results.)
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2375"
|
|
HREF="node123.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2369"
|
|
HREF="node116.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2363"
|
|
HREF="node121.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2371"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2373"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2376"
|
|
HREF="node123.html">Time-varying complex comb filter:</A>
|
|
<B> Up:</B> <A ID="tex2html2370"
|
|
HREF="node116.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html2364"
|
|
HREF="node121.html">Order of execution in</A>
|
|
<B> <A ID="tex2html2372"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2374"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
|