150 lines
5.9 KiB
HTML
150 lines
5.9 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
||
|
|
|
||
|
|
<!--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>
|
||
|
|
<TITLE>Envelope followers</TITLE>
|
||
|
|
<META NAME="description" CONTENT="Envelope followers">
|
||
|
|
<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="node159.html">
|
||
|
|
<LINK REL="previous" HREF="node157.html">
|
||
|
|
<LINK REL="up" HREF="node155.html">
|
||
|
|
<LINK REL="next" HREF="node159.html">
|
||
|
|
</HEAD>
|
||
|
|
|
||
|
|
<BODY >
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html2931"
|
||
|
|
HREF="node159.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html2925"
|
||
|
|
HREF="node155.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html2919"
|
||
|
|
HREF="node157.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html2927"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html2929"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html2932"
|
||
|
|
HREF="node159.html">Single sideband modulation</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html2926"
|
||
|
|
HREF="node155.html">Examples</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html2920"
|
||
|
|
HREF="node157.html">Prefabricated time-varying band-pass filter</A>
|
||
|
|
<B> <A NAME="tex2html2928"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html2930"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<BR>
|
||
|
|
<BR>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
|
||
|
|
<H2><A NAME="SECTION001253000000000000000">
|
||
|
|
Envelope followers</A>
|
||
|
|
</H2>
|
||
|
|
<A NAME="sect8.heterodyning"></A>
|
||
|
|
<P>
|
||
|
|
Example H06.envelope.follower.pd shows a simple and self-explanatory realization of the
|
||
|
|
envelope follower described in Section <A HREF="node153.html#sect8.envelopefollower">8.4.2</A>. An
|
||
|
|
interesting application of envelope following is shown in Example H07.measure.spectrum.pd (Figure <A HREF="#fig08.30">8.30</A>, part a). A famous bell sample is looped as a test
|
||
|
|
sound. Rather than get the overall mean square power of the bell, we would
|
||
|
|
like to estimate the frequency and power of each of its partials. To do this
|
||
|
|
we sweep a band-pass filter up and down in frequency, listening to the result
|
||
|
|
and/or watching the filter's output power using an envelope follower. (We use
|
||
|
|
two band-pass filters in series for better isolation of the partials; this is
|
||
|
|
not especially good filter design practice but it will do in this context.)
|
||
|
|
When the filter is tuned to a partial the envelope follower reports its
|
||
|
|
strength.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
|
||
|
|
<DIV ALIGN="CENTER"><A NAME="fig08.30"></A><A NAME="10622"></A>
|
||
|
|
<TABLE>
|
||
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.30:</STRONG>
|
||
|
|
Analyzing the spectrum of a sound: (a) band-pass filtering a sampled
|
||
|
|
bell sound and envelope-following the result; (b) frequency-shifting a
|
||
|
|
partial to DC and reading off its real and imaginary part.
|
||
|
|
</CAPTION>
|
||
|
|
<TR><TD><IMG
|
||
|
|
WIDTH="524" HEIGHT="435" BORDER="0"
|
||
|
|
SRC="img1025.png"
|
||
|
|
ALT="\begin{figure}\psfig{file=figs/fig08.30.ps}\end{figure}"></TD></TR>
|
||
|
|
</TABLE>
|
||
|
|
</DIV>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
Example H08.heterodyning.pd (part (b) of the figure) shows an alternative way of finding partial strengths of
|
||
|
|
an incoming sound; it has the advantage of reporting the phase as well as the
|
||
|
|
strength. First we modulate the desired partial down to zero frequency. We use
|
||
|
|
a complex-valued sinusoid as a modulator so that we get only one sideband for
|
||
|
|
each component of the input. The test frequency is the only frequency that is
|
||
|
|
modulated to DC; others go elsewhere. We then low-pass the resulting complex
|
||
|
|
signal. (We can use a real-valued low-pass filter separately on the real
|
||
|
|
and imaginary parts.) This essentially removes all the partials except for the
|
||
|
|
DC one, which we then harvest. This technique is the basis of Fourier
|
||
|
|
analysis, the subject of Chapter 9.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
<HR>
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html2931"
|
||
|
|
HREF="node159.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html2925"
|
||
|
|
HREF="node155.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html2919"
|
||
|
|
HREF="node157.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html2927"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html2929"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html2932"
|
||
|
|
HREF="node159.html">Single sideband modulation</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html2926"
|
||
|
|
HREF="node155.html">Examples</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html2920"
|
||
|
|
HREF="node157.html">Prefabricated time-varying band-pass filter</A>
|
||
|
|
<B> <A NAME="tex2html2928"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html2930"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
<ADDRESS>
|
||
|
|
Miller Puckette
|
||
|
|
2006-12-30
|
||
|
|
</ADDRESS>
|
||
|
|
</BODY>
|
||
|
|
</HTML>
|