replace '<A NAME=' with '<A ID='
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node110.html
58
node110.html
@@ -30,42 +30,42 @@ 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="tex2html2199"
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<A ID="tex2html2199"
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HREF="node111.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="tex2html2193"
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<A ID="tex2html2193"
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HREF="node104.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="tex2html2187"
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<A ID="tex2html2187"
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HREF="node109.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="tex2html2195"
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<A ID="tex2html2195"
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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="tex2html2197"
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<A ID="tex2html2197"
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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="tex2html2200"
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<B> Next:</B> <A ID="tex2html2200"
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HREF="node111.html">Artificial reverberation</A>
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<B> Up:</B> <A NAME="tex2html2194"
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<B> Up:</B> <A ID="tex2html2194"
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HREF="node104.html">Time shifts and delays</A>
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<B> Previous:</B> <A NAME="tex2html2188"
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<B> Previous:</B> <A ID="tex2html2188"
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HREF="node109.html">Recirculating delay networks</A>
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<B> <A NAME="tex2html2196"
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<B> <A ID="tex2html2196"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html2198"
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<B> <A ID="tex2html2198"
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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="SECTION001150000000000000000">
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<H1><A ID="SECTION001150000000000000000">
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Power conservation and complex delay networks</A>
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</H1>
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@@ -90,7 +90,7 @@ the gain, suitably defined, is exactly one.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.11"></A><A NAME="8003"></A>
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<DIV ALIGN="CENTER"><A ID="fig07.11"></A><A ID="8003"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.11:</STRONG>
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First fundamental building block for unitary delay networks:
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@@ -163,7 +163,7 @@ where <IMG
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It turns out that a wide range of interesting delay networks has the property
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that the total power output equals the total power input;
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they are called
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<A NAME="8013"></A><I>unitary</I>. To start with, we can put any number of delays in parallel, as
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<A ID="8013"></A><I>unitary</I>. To start with, we can put any number of delays in parallel, as
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shown in Figure <A HREF="#fig07.11">7.11</A>. Whatever the total power of the inputs,
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the total power of the outputs has to equal it.
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@@ -233,7 +233,7 @@ of a collection of signals must must be preserved by rotation.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.12"></A><A NAME="8024"></A>
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<DIV ALIGN="CENTER"><A ID="fig07.12"></A><A ID="8024"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.12:</STRONG>
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Second fundamental building block for unitary delay networks:
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@@ -329,7 +329,7 @@ s = \sin(\theta)
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<BR CLEAR="ALL">
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<P></P>
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for an
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<A NAME="8036"></A><I>angle of rotation</I> <IMG
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<A ID="8036"></A><I>angle of rotation</I> <IMG
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WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img634.png"
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ALT="$\theta$">.
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@@ -423,7 +423,7 @@ unit magnitude and argument <IMG
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<P>
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If we perform a rotation on a pair of signals and then invert one (but not the
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other) of them, the result is a
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<A NAME="8050"></A>
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<A ID="8050"></A>
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<I>reflection</I>.
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This also preserves total signal power, since we can invert any or all of a
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collection of signals without changing the total power. In two dimensions, a
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@@ -486,7 +486,7 @@ a) because each signal need only be multiplied by the one quantity <IMG
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.13"></A><A NAME="8389"></A>
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<DIV ALIGN="CENTER"><A ID="fig07.13"></A><A ID="8389"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.13:</STRONG>
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Details about rotation (and reflection) matrix operations: (a)
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@@ -535,7 +535,7 @@ recirculating networks that still enjoy flat frequency responses.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig07.14"></A><A NAME="8069"></A>
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<DIV ALIGN="CENTER"><A ID="fig07.14"></A><A ID="8069"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.14:</STRONG>
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Flat frequency response in recirculating networks: (a) in general,
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@@ -655,7 +655,7 @@ let the transformation <IMG
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WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img31.png"
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ALT="$W$"> output, the result is the well-known
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<A NAME="8086"></A><A NAME="8087"></A><I>all-pass filter</I>.
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<A ID="8086"></A><A ID="8087"></A><I>all-pass filter</I>.
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With some juggling, and letting <!-- MATH
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$c = \cos(\theta)$
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-->
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@@ -670,36 +670,36 @@ of which we will visit later in this book.
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<P>
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<HR>
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<A NAME="tex2html2199"
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<A ID="tex2html2199"
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HREF="node111.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="tex2html2193"
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<A ID="tex2html2193"
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HREF="node104.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="tex2html2187"
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<A ID="tex2html2187"
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HREF="node109.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="tex2html2195"
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<A ID="tex2html2195"
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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="tex2html2197"
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<A ID="tex2html2197"
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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="tex2html2200"
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<B> Next:</B> <A ID="tex2html2200"
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HREF="node111.html">Artificial reverberation</A>
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<B> Up:</B> <A NAME="tex2html2194"
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<B> Up:</B> <A ID="tex2html2194"
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HREF="node104.html">Time shifts and delays</A>
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<B> Previous:</B> <A NAME="tex2html2188"
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<B> Previous:</B> <A ID="tex2html2188"
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HREF="node109.html">Recirculating delay networks</A>
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<B> <A NAME="tex2html2196"
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<B> <A ID="tex2html2196"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html2198"
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<B> <A ID="tex2html2198"
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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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