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>Single sideband modulation</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Single sideband modulation">
|
|
|
|
|
<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="node160.html">
|
|
|
|
|
<LINK REL="previous" HREF="node158.html">
|
|
|
|
|
<LINK REL="up" HREF="node155.html">
|
|
|
|
|
<LINK REL="next" HREF="node160.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2945"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node160.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 23:32:40 -03:00
|
|
|
<A ID="tex2html2939"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node155.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 23:32:40 -03:00
|
|
|
<A ID="tex2html2933"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node158.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 23:32:40 -03:00
|
|
|
<A ID="tex2html2941"
|
2022-04-12 21:54:18 -03:00
|
|
|
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 23:32:40 -03:00
|
|
|
<A ID="tex2html2943"
|
2022-04-12 21:54:18 -03:00
|
|
|
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>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html2946"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node160.html">Using elementary filters directly:</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html2940"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node155.html">Examples</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html2934"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node158.html">Envelope followers</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2942"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2944"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<H2><A ID="SECTION001254000000000000000">
|
2022-04-12 21:54:18 -03:00
|
|
|
Single sideband modulation</A>
|
|
|
|
|
</H2>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<DIV ALIGN="CENTER"><A ID="fig08.31"></A><A ID="10628"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.31:</STRONG>
|
|
|
|
|
Using an all-pass filter network to
|
|
|
|
|
make a frequency shifter.
|
|
|
|
|
</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="506" HEIGHT="289" BORDER="0"
|
|
|
|
|
SRC="img1026.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig08.31.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
As described in Section <A HREF="node154.html#sect8.singlesideband">8.4.3</A>, a pair of all-pass filters
|
|
|
|
|
can be constructed to give roughly <IMG
|
|
|
|
|
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img5.png"
|
|
|
|
|
ALT="$\pi /2$"> phase difference for positive
|
|
|
|
|
frequencies and <IMG
|
|
|
|
|
WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img283.png"
|
|
|
|
|
ALT="$-\pi/2$"> for negative ones. The design of these pairs is
|
|
|
|
|
beyond the scope of this discussion (see, for instance, [<A
|
|
|
|
|
HREF="node202.html#r-mitra93">Reg93</A>]) but
|
|
|
|
|
Pd does provide an abstraction, <TT>hilbert~</TT>, to do this. Example
|
|
|
|
|
H09.ssb.modulation.pd, shown in Figure <A HREF="#fig08.31">8.31</A>, demonstrates how to use the
|
|
|
|
|
<TT>hilbert~</TT> abstraction to do signal sideband modulation. The
|
|
|
|
|
Hilbert transform dates to the analog era [<A
|
|
|
|
|
HREF="node202.html#r-strange72">Str95</A>, pp.129-132].
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The two outputs of <TT>hilbert~</TT>, considered as the real and imaginary parts
|
|
|
|
|
of a complex-valued signal, are multiplied by a complex sinusoid (at
|
|
|
|
|
right in the figure), and the real part is output. The components of the
|
|
|
|
|
resulting signal are those of the input shifted by a (positive or negative)
|
|
|
|
|
frequency specified in the number box.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<BR><HR>
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
