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.
162 lines
5.3 KiB
162 lines
5.3 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>Elementary filters</TITLE>
|
|
<META NAME="description" CONTENT="Elementary filters">
|
|
<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="node139.html">
|
|
<LINK REL="previous" HREF="node128.html">
|
|
<LINK REL="up" HREF="node127.html">
|
|
<LINK REL="next" HREF="node133.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2547"
|
|
HREF="node133.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2541"
|
|
HREF="node127.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2535"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2543"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2545"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2548"
|
|
HREF="node133.html">Elementary non-recirculating filter</A>
|
|
<B> Up:</B> <A ID="tex2html2542"
|
|
HREF="node127.html">Filters</A>
|
|
<B> Previous:</B> <A ID="tex2html2536"
|
|
HREF="node131.html">Equalizing filters</A>
|
|
<B> <A ID="tex2html2544"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2546"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H1><A ID="SECTION001220000000000000000">
|
|
Elementary filters</A>
|
|
</H1>
|
|
|
|
<P>
|
|
We saw in Chapter 7 how to predict the frequency and phase response of delay
|
|
networks. The art of filter design lies in finding a delay network whose
|
|
transfer function (which controls the frequency and phase response) has a
|
|
desired shape. We will develop an approach to building such delay networks
|
|
out of the two types of comb filters developed in Chapter 7: recirculating and
|
|
non-recirculating. Here we will be interested in the special case where the
|
|
delay is only one sample in length. In this situation, the frequency responses
|
|
shown in Figures <A HREF="node108.html#fig07.06">7.6</A> and <A HREF="node109.html#fig07.10">7.10</A> no longer look like combs;
|
|
the second peak recedes all the way to the sample rate, <IMG
|
|
WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img16.png"
|
|
ALT="$2\pi $"> radians, when
|
|
<IMG
|
|
WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img736.png"
|
|
ALT="$d=1$">. Since only frequencies between 0 and the Nyquist frequency (<IMG
|
|
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img41.png"
|
|
ALT="$\pi $">
|
|
radians) are audible, in effect there is only one peak when <IMG
|
|
WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img736.png"
|
|
ALT="$d=1$">.
|
|
|
|
<P>
|
|
In the comb filters shown in Chapter 7, the peaks are situated at DC (zero
|
|
frequency), but we will often wish to place them at other, nonzero
|
|
frequencies. This is done using delay networks--comb
|
|
filters--with complex-valued gains.
|
|
|
|
<P>
|
|
<BR><HR>
|
|
<!--Table of Child-Links-->
|
|
<A ID="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
|
|
|
<UL>
|
|
<LI><A ID="tex2html2549"
|
|
HREF="node133.html">Elementary non-recirculating filter</A>
|
|
<LI><A ID="tex2html2550"
|
|
HREF="node134.html">Non-recirculating filter, second form</A>
|
|
<LI><A ID="tex2html2551"
|
|
HREF="node135.html">Elementary recirculating filter</A>
|
|
<LI><A ID="tex2html2552"
|
|
HREF="node136.html">Compound filters</A>
|
|
<LI><A ID="tex2html2553"
|
|
HREF="node137.html">Real outputs from complex filters</A>
|
|
<LI><A ID="tex2html2554"
|
|
HREF="node138.html">Two recirculating filters for the price of one</A>
|
|
</UL>
|
|
<!--End of Table of Child-Links-->
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2547"
|
|
HREF="node133.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2541"
|
|
HREF="node127.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2535"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2543"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2545"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2548"
|
|
HREF="node133.html">Elementary non-recirculating filter</A>
|
|
<B> Up:</B> <A ID="tex2html2542"
|
|
HREF="node127.html">Filters</A>
|
|
<B> Previous:</B> <A ID="tex2html2536"
|
|
HREF="node131.html">Equalizing filters</A>
|
|
<B> <A ID="tex2html2544"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2546"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
|