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133 lines
3.6 KiB
133 lines
3.6 KiB
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HREF="node137.html">Real outputs from complex</A>
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HREF="node135.html">Elementary recirculating filter</A>
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<H2><A ID="SECTION001224000000000000000">
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Compound filters</A>
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</H2>
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<P>
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We can use the recirculating and non-recirculating filters developed here to
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create a
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<A ID="10201"></A><A ID="10202"></A><I>compound filter</I> by putting several elementary ones in series. If the parameters
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of the non-recirculating ones (of the first type) are <!-- MATH
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${Q_1}, \ldots, {Q_j}$
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-->
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<IMG
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WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img887.png"
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ALT="${Q_1}, \ldots, {Q_j}$">
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and those of the recirculating ones are <!-- MATH
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${P_1}, \ldots, {P_k}$
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-->
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<IMG
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WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img888.png"
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ALT="${P_1}, \ldots, {P_k}$">, then putting
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them all in series, in any order, will give the transfer function:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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H(Z) = {
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{
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(1 - {Q_1}{Z^{-1}}) \cdots (1 - {Q_j}{Z^{-1}})
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} \over {
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(1 - {P_1}{Z^{-1}}) \cdots (1 - {P_k}{Z^{-1}})
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}
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}
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\end{displaymath}
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-->
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<IMG
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WIDTH="263" HEIGHT="45" BORDER="0"
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SRC="img889.png"
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ALT="\begin{displaymath}
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H(Z) = {
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{
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(1 - {Q_1}{Z^{-1}}) \cdots (1 - {Q_j}{Z^{-1}})
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} \over {
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(1 - {P_1}{Z^{-1}}) \cdots (1 - {P_k}{Z^{-1}})
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}
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}
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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The frequency response of the resulting compound filter is the product of
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those of
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the elementary ones. (One could also combine elementary filters by adding
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their outputs, or making more complicated networks of them; but for most
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purposes the series configuration is the easiest one to work with.)
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<P>
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<BR><HR>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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</ADDRESS>
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