You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
149 lines
4.0 KiB
149 lines
4.0 KiB
<!DOCTYPE html>
|
|
|
|
<!--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>
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
<TITLE>Peaking and stop-band filter</TITLE>
|
|
<META NAME="description" CONTENT="Peaking and stop-band filter">
|
|
<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="node145.html">
|
|
<LINK REL="previous" HREF="node143.html">
|
|
<LINK REL="up" HREF="node139.html">
|
|
<LINK REL="next" HREF="node145.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2730"
|
|
HREF="node145.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2724"
|
|
HREF="node139.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2718"
|
|
HREF="node143.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2726"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2728"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2731"
|
|
HREF="node145.html">Butterworth filters</A>
|
|
<B> Up:</B> <A ID="tex2html2725"
|
|
HREF="node139.html">Designing filters</A>
|
|
<B> Previous:</B> <A ID="tex2html2719"
|
|
HREF="node143.html">Band-pass filter</A>
|
|
<B> <A ID="tex2html2727"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2729"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A ID="SECTION001235000000000000000"></A>
|
|
<A ID="sect8.peaking"></A>
|
|
<BR>
|
|
Peaking and stop-band filter
|
|
</H2>
|
|
|
|
<P>
|
|
In the same way, a peaking filter is obtained from a shelving filter by rotating the
|
|
pole and the zero, and by providing a conjugate pole and zero, as shown in
|
|
Figure <A HREF="#fig08.16">8.16</A>. If the desired center frequency is <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img27.png"
|
|
ALT="$\omega $">, and
|
|
the radii of the pole and zero (as for the shelving filter) are
|
|
<IMG
|
|
WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img57.png"
|
|
ALT="$p$"> and <IMG
|
|
WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img592.png"
|
|
ALT="$q$">, then we place the the upper pole and zero at
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
{P_1} = p \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="164" HEIGHT="28" BORDER="0"
|
|
SRC="img925.png"
|
|
ALT="\begin{displaymath}
|
|
{P_1} = p \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
{Q_1} = q \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="166" HEIGHT="28" BORDER="0"
|
|
SRC="img926.png"
|
|
ALT="\begin{displaymath}
|
|
{Q_1} = q \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
As a special case, placing the zero on the unit circle gives a stop-band filter;
|
|
in this case the gain at the center frequency is zero. This is analogous
|
|
to the one-pole, one-zero high-pass filter above.
|
|
|
|
<P>
|
|
|
|
<DIV ALIGN="CENTER"><A ID="fig08.16"></A><A ID="10371"></A>
|
|
<TABLE>
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.16:</STRONG>
|
|
A peaking filter: (a) pole-zero diagram; (b)
|
|
frequency response. Here the filter is set to attenuate by 6 decibels at
|
|
the center frequency.</CAPTION>
|
|
<TR><TD><IMG
|
|
WIDTH="536" HEIGHT="245" BORDER="0"
|
|
SRC="img927.png"
|
|
ALT="\begin{figure}\psfig{file=figs/fig08.16.ps}\end{figure}"></TD></TR>
|
|
</TABLE>
|
|
</DIV>
|
|
|
|
<P>
|
|
<BR><HR>
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
|