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215 lines
7.2 KiB
215 lines
7.2 KiB
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<H2><A ID="SECTION001255000000000000000">
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Using elementary filters directly: shelving and peaking</A>
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</H2>
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<P>
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<DIV ALIGN="CENTER"><A ID="fig08.32"></A><A ID="10641"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.32:</STRONG>
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Building filters from elementary, raw ones: (a) shelving; (b) peaking.
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</CAPTION>
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<TR><TD><IMG
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WIDTH="548" HEIGHT="276" BORDER="0"
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SRC="img1027.png"
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ALT="\begin{figure}\psfig{file=figs/fig08.32.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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No finite set of prefabricated filters could fill every possible need, and so
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Pd provides the elementary filters of Sections
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<A HREF="node133.html#sect8.nonrecirculating">8.2.1</A>-<A HREF="node135.html#sect8.recirculating">8.2.3</A> in raw form, so that the
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user can supply the filter coefficients explicitly. In this section we will
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describe patches that realize the shelving and peaking filters of Sections
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<A HREF="node142.html#sect8.shelving">8.3.3</A> and <A HREF="node144.html#sect8.peaking">8.3.5</A> directly from elementary filters.
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First we introduce the six Pd objects that realize elementary filters:
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<P>
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<BR><!-- MATH
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$\fbox{ \texttt{rzero\~}}$
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-->
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<IMG
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WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1028.png"
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ALT="\fbox{ \texttt{rzero\~}}">,
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<BR><!-- MATH
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$\fbox{ \texttt{rzero\_rev\~}}$
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-->
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<IMG
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WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1029.png"
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ALT="\fbox{ \texttt{rzero\_rev\~}}">,
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<BR><!-- MATH
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$\fbox{ \texttt{rpole\~}}$
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-->
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<IMG
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WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1030.png"
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ALT="\fbox{ \texttt{rpole\~}}">:
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<A ID="10847"></A><A ID="10848"></A><A ID="10849"></A>elementary filters with real-valued coefficients operating on real-valued
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signals. The three implement non-recirculating filters of the first and
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second types, and the recirculating filter. They all have one inlet, at
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right, to supply the coefficient that sets the location of the zero or pole.
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The inlet
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for the coefficient (as well as the left inlet for the signal to filter) take
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audio signals. No stability check is performed.
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<P>
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<BR><!-- MATH
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$\fbox{ \texttt{czero\~}}$
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-->
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<IMG
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WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1034.png"
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ALT="\fbox{ \texttt{czero\~}}">,
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<BR><!-- MATH
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$\fbox{ \texttt{czero\_rev\~}}$
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-->
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<IMG
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WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1035.png"
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ALT="\fbox{ \texttt{czero\_rev\~}}">,
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<BR><!-- MATH
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$\fbox{ \texttt{cpole\~}}$
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-->
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<IMG
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WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1036.png"
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ALT="\fbox{ \texttt{cpole\~}}">:
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<A ID="10850"></A><A ID="10851"></A><A ID="10852"></A>elementary filters with complex-valued coefficients, operating on complex-valued
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signals, corresponding to the real-valued ones above. Instead of two inlets and
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one outlet, each of these filters has four inlets (real and imaginary part of
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the signal to filter, and real and imaginary part of the coefficient) and
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two outlets for the complex-valued output.
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<P>
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The example patches use a pair of abstractions to graph the frequency and phase
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responses of filters as explained in Example H10.measurement.pd. Example H11.shelving.pd (Figure <A HREF="#fig08.32">8.32</A>, part a) shows how to make a shelving filter. One
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elementary non-recirculating filter (<TT>rzero~</TT>) and one elementary
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recirculating one (<TT>rpole~</TT>) are put in series. As the analysis of
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Section <A HREF="node148.html#sect8.timevarying">8.3.9</A> might suggest, the <TT>rzero~</TT> object is placed
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first.
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<P>
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Example H12.peaking.pd (part (b) of the figure) implements a peaking filter. Here the
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pole and the zero are rotated by an angle <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img27.png"
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ALT="$\omega $"> to control the center
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frequency of the filter. The bandwidth and center frequency gain are equal to
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the shelf frequency and the DC gain of the corresponding shelving filter.
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<P>
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Example H13.butterworth.pd demonstrates a three-pole, three-zero Butterworth shelving
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filter. The filter itself is an abstraction, <TT>butterworth3~</TT>, for
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easy reuse.
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<P>
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<B> Next:</B> <A ID="tex2html2960"
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HREF="node161.html">Making and using all-pass</A>
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<B> Up:</B> <A ID="tex2html2954"
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HREF="node155.html">Examples</A>
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<B> Previous:</B> <A ID="tex2html2948"
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HREF="node159.html">Single sideband modulation</A>
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<B> <A ID="tex2html2956"
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HREF="node4.html">Contents</A></B>
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HREF="node201.html">Index</A></B>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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