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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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2022-04-12 21:54:18 -03:00
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<TITLE>Exercises</TITLE>
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<B> Next:</B> <A NAME="tex2html2984"
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HREF="node163.html">Fourier analysis and resynthesis</A>
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<B> Up:</B> <A NAME="tex2html2978"
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HREF="node127.html">Filters</A>
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<B> Previous:</B> <A NAME="tex2html2974"
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HREF="node161.html">Making and using all-pass</A>
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<B> <A NAME="tex2html2980"
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<H1><A NAME="SECTION001260000000000000000">
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Exercises</A>
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</H1>
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<P>
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<OL>
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<LI>A recirculating elementary filter has a pole at <IMG
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WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1041.png"
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ALT="$i/2$">. At what angular
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frequency is its gain greatest, and what is the gain there? At what angular
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frequency is the gain least, and what is the gain there?
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<P>
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</LI>
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<LI>A shelving filter has a pole at 0.9 and a zero at 0.8. What are: the DC
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gain; the gain at Nyquist; the approximate transition frequency?
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<P>
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</LI>
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<LI>Suppose a complex recirculating filter has a pole at <IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img880.png"
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ALT="$P$">. Suppose
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further that you want to combine its real and imaginary output to make a
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single, real-valued signal equivalent to a two-pole filter with poles at <IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img880.png"
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ALT="$P$">
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and <IMG
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WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img890.png"
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ALT="$\overline{P}$">. How would you weight the two outputs?
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<P>
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</LI>
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<LI>Suppose you wish to design a peaking filter with gain 2 at 1000 Hertz and
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bandwidth 200 Hertz (at a sample rate of 44100 Hertz). Where, approximately,
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would you put the upper pole and zero?
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<P>
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</LI>
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<LI>In the same situation, where would you put the (upper) pole and zero
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to remove a sinusoid at 1000 Hertz entirely, while attenuating only 3 decibels
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at 1001 Hertz?
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<P>
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</LI>
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<LI>A one-pole complex filter is excited by an impulse to make a tone at 1000
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Hertz, which decays 10 decibels in one second (at a sample rate of 44100
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Hertz). Where would you place the pole? What is the value of ``q"?
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<P>
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</LI>
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</OL>
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<BR>
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<B> Next:</B> <A NAME="tex2html2984"
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HREF="node163.html">Fourier analysis and resynthesis</A>
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<B> Up:</B> <A NAME="tex2html2978"
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HREF="node127.html">Filters</A>
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<B> Previous:</B> <A NAME="tex2html2974"
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HREF="node161.html">Making and using all-pass</A>
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<B> <A NAME="tex2html2980"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html2982"
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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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