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119 lines
3.7 KiB
119 lines
3.7 KiB
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original version by: Nikos Drakos, CBLU, University of Leeds
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HREF="node160.html">Using elementary filters directly:</A>
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<H2><A ID="SECTION001254000000000000000">
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Single sideband modulation</A>
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</H2>
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<P>
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<DIV ALIGN="CENTER"><A ID="fig08.31"></A><A ID="10628"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.31:</STRONG>
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Using an all-pass filter network to
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make a frequency shifter.
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</CAPTION>
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<TR><TD><IMG
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WIDTH="506" HEIGHT="289" BORDER="0"
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SRC="img1026.png"
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ALT="\begin{figure}\psfig{file=figs/fig08.31.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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As described in Section <A HREF="node154.html#sect8.singlesideband">8.4.3</A>, a pair of all-pass filters
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can be constructed to give roughly <IMG
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WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img5.png"
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ALT="$\pi /2$"> phase difference for positive
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frequencies and <IMG
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WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img283.png"
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ALT="$-\pi/2$"> for negative ones. The design of these pairs is
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beyond the scope of this discussion (see, for instance, [<A
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HREF="node202.html#r-mitra93">Reg93</A>]) but
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Pd does provide an abstraction, <TT>hilbert~</TT>, to do this. Example
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H09.ssb.modulation.pd, shown in Figure <A HREF="#fig08.31">8.31</A>, demonstrates how to use the
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<TT>hilbert~</TT> abstraction to do signal sideband modulation. The
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Hilbert transform dates to the analog era [<A
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HREF="node202.html#r-strange72">Str95</A>, pp.129-132].
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<P>
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The two outputs of <TT>hilbert~</TT>, considered as the real and imaginary parts
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of a complex-valued signal, are multiplied by a complex sinusoid (at
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right in the figure), and the real part is output. The components of the
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resulting signal are those of the input shifted by a (positive or negative)
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frequency specified in the number box.
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<P>
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<BR><HR>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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</ADDRESS>
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