163 lines
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163 lines
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<H1><A NAME="SECTION001220000000000000000">
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Elementary filters</A>
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</H1>
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<P>
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We saw in Chapter 7 how to predict the frequency and phase response of delay
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networks. The art of filter design lies in finding a delay network whose
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transfer function (which controls the frequency and phase response) has a
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desired shape. We will develop an approach to building such delay networks
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out of the two types of comb filters developed in Chapter 7: recirculating and
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non-recirculating. Here we will be interested in the special case where the
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delay is only one sample in length. In this situation, the frequency responses
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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;
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the second peak recedes all the way to the sample rate, <IMG
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WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img16.png"
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ALT="$2\pi $"> radians, when
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<IMG
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WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img736.png"
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ALT="$d=1$">. Since only frequencies between 0 and the Nyquist frequency (<IMG
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SRC="img41.png"
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ALT="$\pi $">
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radians) are audible, in effect there is only one peak when <IMG
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WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img736.png"
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ALT="$d=1$">.
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<P>
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In the comb filters shown in Chapter 7, the peaks are situated at DC (zero
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frequency), but we will often wish to place them at other, nonzero
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frequencies. This is done using delay networks--comb
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filters--with complex-valued gains.
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html2549"
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HREF="node133.html">Elementary non-recirculating filter</A>
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<LI><A NAME="tex2html2550"
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HREF="node134.html">Non-recirculating filter, second form</A>
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<LI><A NAME="tex2html2551"
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HREF="node135.html">Elementary recirculating filter</A>
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<LI><A NAME="tex2html2552"
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HREF="node136.html">Compound filters</A>
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<LI><A NAME="tex2html2553"
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HREF="node137.html">Real outputs from complex filters</A>
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<LI><A NAME="tex2html2554"
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HREF="node138.html">Two recirculating filters for the price of one</A>
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HREF="node133.html">Elementary non-recirculating filter</A>
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<B> Up:</B> <A NAME="tex2html2542"
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HREF="node127.html">Filters</A>
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<B> Previous:</B> <A NAME="tex2html2536"
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HREF="node131.html">Equalizing filters</A>
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<B> <A NAME="tex2html2544"
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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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