<!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 NAME="tex2html2547" HREF="node133.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html2541" HREF="node127.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html2535" HREF="node131.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html2543" HREF="node4.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A NAME="tex2html2545" HREF="node201.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> <BR> <B> Next:</B> <A NAME="tex2html2548" HREF="node133.html">Elementary non-recirculating filter</A> <B> Up:</B> <A NAME="tex2html2542" HREF="node127.html">Filters</A> <B> Previous:</B> <A NAME="tex2html2536" HREF="node131.html">Equalizing filters</A> <B> <A NAME="tex2html2544" HREF="node4.html">Contents</A></B> <B> <A NAME="tex2html2546" HREF="node201.html">Index</A></B> <BR> <BR> <!--End of Navigation Panel--> <H1><A NAME="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 NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A> <UL> <LI><A NAME="tex2html2549" HREF="node133.html">Elementary non-recirculating filter</A> <LI><A NAME="tex2html2550" HREF="node134.html">Non-recirculating filter, second form</A> <LI><A NAME="tex2html2551" HREF="node135.html">Elementary recirculating filter</A> <LI><A NAME="tex2html2552" HREF="node136.html">Compound filters</A> <LI><A NAME="tex2html2553" HREF="node137.html">Real outputs from complex filters</A> <LI><A NAME="tex2html2554" HREF="node138.html">Two recirculating filters for the price of one</A> </UL> <!--End of Table of Child-Links--> <HR> <!--Navigation Panel--> <A NAME="tex2html2547" HREF="node133.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html2541" HREF="node127.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html2535" HREF="node131.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html2543" HREF="node4.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A NAME="tex2html2545" HREF="node201.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> <BR> <B> Next:</B> <A NAME="tex2html2548" HREF="node133.html">Elementary non-recirculating filter</A> <B> Up:</B> <A NAME="tex2html2542" HREF="node127.html">Filters</A> <B> Previous:</B> <A NAME="tex2html2536" HREF="node131.html">Equalizing filters</A> <B> <A NAME="tex2html2544" HREF="node4.html">Contents</A></B> <B> <A NAME="tex2html2546" HREF="node201.html">Index</A></B> <!--End of Navigation Panel--> <ADDRESS> Miller Puckette 2006-12-30 </ADDRESS> </BODY> </HTML>