2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
|
<!--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>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<TITLE>Time-varying complex comb filter: shakers</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Time-varying complex comb filter: shakers">
|
|
|
|
|
<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="node124.html">
|
|
|
|
|
<LINK REL="previous" HREF="node122.html">
|
|
|
|
|
<LINK REL="up" HREF="node116.html">
|
|
|
|
|
<LINK REL="next" HREF="node124.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html2389"
|
|
|
|
|
HREF="node124.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2383"
|
|
|
|
|
HREF="node116.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2377"
|
|
|
|
|
HREF="node122.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2385"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2387"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html2390"
|
|
|
|
|
HREF="node124.html">Reverberator</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html2384"
|
|
|
|
|
HREF="node116.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html2378"
|
|
|
|
|
HREF="node122.html">Non-recirculating comb filter as</A>
|
|
|
|
|
<B> <A NAME="tex2html2386"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html2388"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
<H2><A NAME="SECTION0011107000000000000000">
|
|
|
|
|
Time-varying complex comb filter: shakers</A>
|
|
|
|
|
</H2>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Example G07.shaker.pd (Figure <A HREF="#fig07.30">7.30</A>) shows a different way of extending the
|
|
|
|
|
idea of a comb filter. Here we combine the input signal at four different
|
|
|
|
|
time shifts (instead of two, as in the original non-recirculating comb filter),
|
|
|
|
|
each at a different positive or negative gain. To do this, we insert the
|
|
|
|
|
input signal into a delay line and tap it at three different points; the
|
|
|
|
|
fourth ``tap" is the original, un-delayed signal.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
|
|
|
|
<DIV ALIGN="CENTER"><A NAME="fig07.30"></A><A NAME="8287"></A>
|
|
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.30:</STRONG>
|
|
|
|
|
A ``shaker", a four-tap comb filter with randomly varying gains
|
|
|
|
|
on the taps.</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="591" HEIGHT="386" BORDER="0"
|
|
|
|
|
SRC="img845.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig07.30.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
As a way of thinking about the frequency response of a four-tap comb filter,
|
|
|
|
|
we consider first what happens when two of the four gains are close to zero.
|
|
|
|
|
Then we end up with a simple non-recirculating comb filter, with the slight
|
|
|
|
|
complication that the gains of the two delayed copies may be different. If they
|
|
|
|
|
are both of the same sign, we get the same peaks and valleys as predicted
|
|
|
|
|
in Section <A HREF="node108.html#sect7.network">7.3</A>, only with the valleys between peaks possibly
|
|
|
|
|
more shallow. If they are opposite in sign, the valleys become peaks and
|
|
|
|
|
the peaks become valleys.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Depending on which two taps we supposed were nonzero, the peaks and valleys are
|
|
|
|
|
spaced by different amounts; the delay times are chosen so that 6 different
|
|
|
|
|
delay times can arise in this way, ranging between 6 and 30 milliseconds. In
|
|
|
|
|
the general case in which all the gains are non-zero, we can imagine the
|
|
|
|
|
frequency response function varying continuously between these extremes, giving
|
|
|
|
|
a succession of complicated patterns. This has the effect of raising and
|
|
|
|
|
lowering the amplitudes of the partials of the incoming signal, all
|
|
|
|
|
independently of the others, in a complicated pattern, to give a steadily
|
|
|
|
|
time-varying timbre.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The right-hand side of the patch takes care of changing the gains of the
|
|
|
|
|
input signal and its three time-shifted copies. Each time the <TT>metro</TT> object
|
|
|
|
|
fires, a counter is incremented (the <TT>f</TT>, <TT>+ 1</TT>, and
|
|
|
|
|
<TT>mod 4</TT> objects). This controls which of the amplitudes will be changed.
|
|
|
|
|
The amplitude itself is computed by making a random number and normalizing it to
|
|
|
|
|
lie between -0.7 and 1.3 in value. The random value and the index are packed
|
|
|
|
|
(along with a third value, a time interval) and this triple goes to the
|
|
|
|
|
<TT>route</TT> object. The first element of the triple (the
|
|
|
|
|
counter) selects which output to send the other two values to; as a result,
|
|
|
|
|
one of the four possible <TT>line~</TT> objects gets a message to ramp to
|
|
|
|
|
a new value.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
If the time variation is done quickly enough, there is also a modulation
|
|
|
|
|
effect on the original signal; in this situation the straight line segments
|
|
|
|
|
used in this example should be replaced by modulating signals with more
|
|
|
|
|
controllable frequency content, for instance using filters (the
|
|
|
|
|
subject of Chapter 8).
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html2389"
|
|
|
|
|
HREF="node124.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2383"
|
|
|
|
|
HREF="node116.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2377"
|
|
|
|
|
HREF="node122.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2385"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html2387"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html2390"
|
|
|
|
|
HREF="node124.html">Reverberator</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html2384"
|
|
|
|
|
HREF="node116.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html2378"
|
|
|
|
|
HREF="node122.html">Non-recirculating comb filter as</A>
|
|
|
|
|
<B> <A NAME="tex2html2386"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html2388"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
