replace '<A NAME=' with '<A ID='
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node41.html
52
node41.html
@@ -30,43 +30,43 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BODY >
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<!--Navigation Panel-->
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<A NAME="tex2html1161"
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<A ID="tex2html1161"
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HREF="node42.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
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SRC="next.png"></A>
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<A NAME="tex2html1155"
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<A ID="tex2html1155"
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HREF="node40.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
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SRC="up.png"></A>
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<A NAME="tex2html1149"
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<A ID="tex2html1149"
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HREF="node40.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
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SRC="prev.png"></A>
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<A NAME="tex2html1157"
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<A ID="tex2html1157"
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HREF="node4.html">
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
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SRC="contents.png"></A>
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<A NAME="tex2html1159"
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<A ID="tex2html1159"
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HREF="node201.html">
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<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
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SRC="index.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html1162"
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<B> Next:</B> <A ID="tex2html1162"
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HREF="node42.html">Control</A>
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<B> Up:</B> <A NAME="tex2html1156"
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<B> Up:</B> <A ID="tex2html1156"
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HREF="node40.html">Audio and control computations</A>
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<B> Previous:</B> <A NAME="tex2html1150"
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<B> Previous:</B> <A ID="tex2html1150"
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HREF="node40.html">Audio and control computations</A>
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<B> <A NAME="tex2html1158"
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<B> <A ID="tex2html1158"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1160"
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<B> <A ID="tex2html1160"
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HREF="node201.html">Index</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00710000000000000000"></A>
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<A NAME="sect3.sampling"></A>
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<H1><A ID="SECTION00710000000000000000"></A>
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<A ID="sect3.sampling"></A>
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<BR>
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The sampling theorem
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</H1>
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@@ -122,7 +122,7 @@ integers.
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<P>
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It is customary at this point in discussions of computer music to invoke
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the famous
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<A NAME="3554"></A><I>Nyquist theorem</I>.
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<A ID="3554"></A><I>Nyquist theorem</I>.
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This states (roughly speaking) that if a function is a finite or even infinite
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combination of sinusoids, none of whose angular frequencies exceeds <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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@@ -238,7 +238,7 @@ frequency--specifically, you will hear the unique frequency between 0 and <IMG
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that the higher frequency lands on when reduced in the above way. This
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phenomenon is called
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<I>foldover</I>,
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<A NAME="3558"></A>
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<A ID="3558"></A>
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because the half-line of frequencies from 0
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to <IMG
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WIDTH="19" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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@@ -252,7 +252,7 @@ from 0 to <IMG
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SRC="img41.png"
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ALT="$\pi $">. The word
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<I>aliasing</I>
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<A NAME="3560"></A>means the same thing. Figure <A HREF="#fig03.01">3.1</A> shows that sinusoids of angular
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<A ID="3560"></A>means the same thing. Figure <A HREF="#fig03.01">3.1</A> shows that sinusoids of angular
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frequencies <IMG
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WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img5.png"
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@@ -264,7 +264,7 @@ as digital audio signals.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig03.01"></A><A NAME="3564"></A>
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<DIV ALIGN="CENTER"><A ID="fig03.01"></A><A ID="3564"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3.1:</STRONG>
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Two real sinusoids, with angular frequencies <IMG
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@@ -371,36 +371,36 @@ A very non-technical treatment of sampling theory is given in
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<P>
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<HR>
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<!--Navigation Panel-->
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<A NAME="tex2html1161"
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<A ID="tex2html1161"
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HREF="node42.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
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SRC="next.png"></A>
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<A NAME="tex2html1155"
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<A ID="tex2html1155"
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HREF="node40.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
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SRC="up.png"></A>
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<A NAME="tex2html1149"
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<A ID="tex2html1149"
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HREF="node40.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
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SRC="prev.png"></A>
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<A NAME="tex2html1157"
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<A ID="tex2html1157"
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HREF="node4.html">
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
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SRC="contents.png"></A>
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<A NAME="tex2html1159"
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<A ID="tex2html1159"
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HREF="node201.html">
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<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
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SRC="index.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html1162"
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<B> Next:</B> <A ID="tex2html1162"
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HREF="node42.html">Control</A>
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<B> Up:</B> <A NAME="tex2html1156"
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<B> Up:</B> <A ID="tex2html1156"
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HREF="node40.html">Audio and control computations</A>
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<B> Previous:</B> <A NAME="tex2html1150"
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<B> Previous:</B> <A ID="tex2html1150"
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HREF="node40.html">Audio and control computations</A>
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<B> <A NAME="tex2html1158"
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<B> <A ID="tex2html1158"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1160"
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<B> <A ID="tex2html1160"
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HREF="node201.html">Index</A></B>
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<!--End of Navigation Panel-->
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<ADDRESS>
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