<!DOCTYPE html>
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
original version by: Nikos Drakos, CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<TITLE>Exercises</TITLE>
<META NAME="description" CONTENT="Exercises">
<META NAME="keywords" CONTENT="book">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
<LINK REL="STYLESHEET" HREF="book.css">
<LINK REL="previous" HREF="node155.html">
<LINK REL="up" HREF="node127.html">
<LINK REL="next" HREF="node163.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html2983"
HREF="node163.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="next.png"></A>
<A NAME="tex2html2977"
HREF="node127.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="up.png"></A>
<A NAME="tex2html2973"
HREF="node161.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="prev.png"></A>
<A NAME="tex2html2979"
HREF="node4.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="contents.png"></A>
<A NAME="tex2html2981"
HREF="node201.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
SRC="index.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html2984"
HREF="node163.html">Fourier analysis and resynthesis</A>
<B> Up:</B> <A NAME="tex2html2978"
HREF="node127.html">Filters</A>
<B> Previous:</B> <A NAME="tex2html2974"
HREF="node161.html">Making and using all-pass</A>
<B> <A NAME="tex2html2980"
HREF="node4.html">Contents</A></B>
<B> <A NAME="tex2html2982"
HREF="node201.html">Index</A></B>
<BR>
<BR>
<!--End of Navigation Panel-->
<H1><A NAME="SECTION001260000000000000000">
Exercises</A>
</H1>
<P>
<OL>
<LI>A recirculating elementary filter has a pole at <IMG
WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img1041.png"
ALT="$i/2$">. At what angular
frequency is its gain greatest, and what is the gain there? At what angular
frequency is the gain least, and what is the gain there?
<P>
</LI>
<LI>A shelving filter has a pole at 0.9 and a zero at 0.8. What are: the DC
gain; the gain at Nyquist; the approximate transition frequency?
<P>
</LI>
<LI>Suppose a complex recirculating filter has a pole at <IMG
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img880.png"
ALT="$P$">. Suppose
further that you want to combine its real and imaginary output to make a
single, real-valued signal equivalent to a two-pole filter with poles at <IMG
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img880.png"
ALT="$P$">
and <IMG
WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img890.png"
ALT="$\overline{P}$">. How would you weight the two outputs?
<P>
</LI>
<LI>Suppose you wish to design a peaking filter with gain 2 at 1000 Hertz and
bandwidth 200 Hertz (at a sample rate of 44100 Hertz). Where, approximately,
would you put the upper pole and zero?
<P>
</LI>
<LI>In the same situation, where would you put the (upper) pole and zero
to remove a sinusoid at 1000 Hertz entirely, while attenuating only 3 decibels
at 1001 Hertz?
<P>
</LI>
<LI>A one-pole complex filter is excited by an impulse to make a tone at 1000
Hertz, which decays 10 decibels in one second (at a sample rate of 44100
Hertz). Where would you place the pole? What is the value of ``q"?
<P>
</LI>
</OL>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html2983"
HREF="node163.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="next.png"></A>
<A NAME="tex2html2977"
HREF="node127.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="up.png"></A>
<A NAME="tex2html2973"
HREF="node161.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="prev.png"></A>
<A NAME="tex2html2979"
HREF="node4.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="contents.png"></A>
<A NAME="tex2html2981"
HREF="node201.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
SRC="index.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html2984"
HREF="node163.html">Fourier analysis and resynthesis</A>
<B> Up:</B> <A NAME="tex2html2978"
HREF="node127.html">Filters</A>
<B> Previous:</B> <A NAME="tex2html2974"
HREF="node161.html">Making and using all-pass</A>
<B> <A NAME="tex2html2980"
HREF="node4.html">Contents</A></B>
<B> <A NAME="tex2html2982"
HREF="node201.html">Index</A></B>
<!--End of Navigation Panel-->
<ADDRESS>
Miller Puckette
2006-12-30
</ADDRESS>
</BODY>
</HTML>