212 lines
7.6 KiB
HTML
212 lines
7.6 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>Using elementary filters directly: shelving and peaking</TITLE>
|
||
|
|
<META NAME="description" CONTENT="Using elementary filters directly: shelving and peaking">
|
||
|
|
<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="node161.html">
|
||
|
|
<LINK REL="previous" HREF="node159.html">
|
||
|
|
<LINK REL="up" HREF="node155.html">
|
||
|
|
<LINK REL="next" HREF="node161.html">
|
||
|
|
</HEAD>
|
||
|
|
|
||
|
|
<BODY >
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html2959"
|
||
|
|
HREF="node161.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="tex2html2953"
|
||
|
|
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="tex2html2947"
|
||
|
|
HREF="node159.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="tex2html2955"
|
||
|
|
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="tex2html2957"
|
||
|
|
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="tex2html2960"
|
||
|
|
HREF="node161.html">Making and using all-pass</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html2954"
|
||
|
|
HREF="node155.html">Examples</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html2948"
|
||
|
|
HREF="node159.html">Single sideband modulation</A>
|
||
|
|
<B> <A NAME="tex2html2956"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html2958"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<BR>
|
||
|
|
<BR>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
|
||
|
|
<H2><A NAME="SECTION001255000000000000000">
|
||
|
|
Using elementary filters directly: shelving and peaking</A>
|
||
|
|
</H2>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
|
||
|
|
<DIV ALIGN="CENTER"><A NAME="fig08.32"></A><A NAME="10641"></A>
|
||
|
|
<TABLE>
|
||
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.32:</STRONG>
|
||
|
|
Building filters from elementary, raw ones: (a) shelving; (b) peaking.
|
||
|
|
</CAPTION>
|
||
|
|
<TR><TD><IMG
|
||
|
|
WIDTH="548" HEIGHT="276" BORDER="0"
|
||
|
|
SRC="img1027.png"
|
||
|
|
ALT="\begin{figure}\psfig{file=figs/fig08.32.ps}\end{figure}"></TD></TR>
|
||
|
|
</TABLE>
|
||
|
|
</DIV>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
No finite set of prefabricated filters could fill every possible need, and so
|
||
|
|
Pd provides the elementary filters of Sections
|
||
|
|
<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
|
||
|
|
user can supply the filter coefficients explicitly. In this section we will
|
||
|
|
describe patches that realize the shelving and peaking filters of Sections
|
||
|
|
<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.
|
||
|
|
First we introduce the six Pd objects that realize elementary filters:
|
||
|
|
|
||
|
|
<P>
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{rzero\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1028.png"
|
||
|
|
ALT="\fbox{ \texttt{rzero\~}}">,
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{rzero\_rev\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1029.png"
|
||
|
|
ALT="\fbox{ \texttt{rzero\_rev\~}}">,
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{rpole\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1030.png"
|
||
|
|
ALT="\fbox{ \texttt{rpole\~}}">:
|
||
|
|
<A NAME="10847"></A><A NAME="10848"></A><A NAME="10849"></A>elementary filters with real-valued coefficients operating on real-valued
|
||
|
|
signals. The three implement non-recirculating filters of the first and
|
||
|
|
second types, and the recirculating filter. They all have one inlet, at
|
||
|
|
right, to supply the coefficient that sets the location of the zero or pole.
|
||
|
|
The inlet
|
||
|
|
for the coefficient (as well as the left inlet for the signal to filter) take
|
||
|
|
audio signals. No stability check is performed.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{czero\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1034.png"
|
||
|
|
ALT="\fbox{ \texttt{czero\~}}">,
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{czero\_rev\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1035.png"
|
||
|
|
ALT="\fbox{ \texttt{czero\_rev\~}}">,
|
||
|
|
<BR><!-- MATH
|
||
|
|
$\fbox{ \texttt{cpole\~}}$
|
||
|
|
-->
|
||
|
|
<IMG
|
||
|
|
WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img1036.png"
|
||
|
|
ALT="\fbox{ \texttt{cpole\~}}">:
|
||
|
|
<A NAME="10850"></A><A NAME="10851"></A><A NAME="10852"></A>elementary filters with complex-valued coefficients, operating on complex-valued
|
||
|
|
signals, corresponding to the real-valued ones above. Instead of two inlets and
|
||
|
|
one outlet, each of these filters has four inlets (real and imaginary part of
|
||
|
|
the signal to filter, and real and imaginary part of the coefficient) and
|
||
|
|
two outlets for the complex-valued output.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
The example patches use a pair of abstractions to graph the frequency and phase
|
||
|
|
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
|
||
|
|
elementary non-recirculating filter (<TT>rzero~</TT>) and one elementary
|
||
|
|
recirculating one (<TT>rpole~</TT>) are put in series. As the analysis of
|
||
|
|
Section <A HREF="node148.html#sect8.timevarying">8.3.9</A> might suggest, the <TT>rzero~</TT> object is placed
|
||
|
|
first.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
Example H12.peaking.pd (part (b) of the figure) implements a peaking filter. Here the
|
||
|
|
pole and the zero are rotated by an angle <IMG
|
||
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
||
|
|
SRC="img27.png"
|
||
|
|
ALT="$\omega $"> to control the center
|
||
|
|
frequency of the filter. The bandwidth and center frequency gain are equal to
|
||
|
|
the shelf frequency and the DC gain of the corresponding shelving filter.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
Example H13.butterworth.pd demonstrates a three-pole, three-zero Butterworth shelving
|
||
|
|
filter. The filter itself is an abstraction, <TT>butterworth3~</TT>, for
|
||
|
|
easy reuse.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
<HR>
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html2959"
|
||
|
|
HREF="node161.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="tex2html2953"
|
||
|
|
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="tex2html2947"
|
||
|
|
HREF="node159.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="tex2html2955"
|
||
|
|
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="tex2html2957"
|
||
|
|
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="tex2html2960"
|
||
|
|
HREF="node161.html">Making and using all-pass</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html2954"
|
||
|
|
HREF="node155.html">Examples</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html2948"
|
||
|
|
HREF="node159.html">Single sideband modulation</A>
|
||
|
|
<B> <A NAME="tex2html2956"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html2958"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
<ADDRESS>
|
||
|
|
Miller Puckette
|
||
|
|
2006-12-30
|
||
|
|
</ADDRESS>
|
||
|
|
</BODY>
|
||
|
|
</HTML>
|