You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
214 lines
5.8 KiB
214 lines
5.8 KiB
<!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="node116.html">
|
|
<LINK REL="up" HREF="node104.html">
|
|
<LINK REL="next" HREF="node127.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2427"
|
|
HREF="node127.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2421"
|
|
HREF="node104.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2417"
|
|
HREF="node125.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2423"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2425"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2428"
|
|
HREF="node127.html">Filters</A>
|
|
<B> Up:</B> <A ID="tex2html2422"
|
|
HREF="node104.html">Time shifts and delays</A>
|
|
<B> Previous:</B> <A ID="tex2html2418"
|
|
HREF="node125.html">Pitch shifter</A>
|
|
<B> <A ID="tex2html2424"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2426"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H1><A ID="SECTION0011110000000000000000">
|
|
Exercises</A>
|
|
</H1>
|
|
|
|
<P>
|
|
|
|
<OL>
|
|
<LI>A complex number has magnitude one and argument <IMG
|
|
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img52.png"
|
|
ALT="$\pi /4$">. What are
|
|
its real and imaginary parts?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>A complex number has magnitude one and real part <IMG
|
|
WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img98.png"
|
|
ALT="$1/2$">. What is its
|
|
imaginary part? (There are two possible values.)
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>What delay time would you give a comb filter so that its first frequency
|
|
response peak is at 440 Hertz? If the sample rate is 44100, what frequency
|
|
would correspond to the nearest integer delay?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Suppose you made a variation on the non-recirculating comb filter so that
|
|
the delayed signal was subtracted from the original instead of adding. What
|
|
would the new frequency response be?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>If you want to make a 6-Hertz vibrato with a sinusoidally varying
|
|
delay line, and if you want the vibrato to change the frequency by 5%, how
|
|
big a delay variation would you need? How would this change if the same
|
|
depth of vibrato was desired at 12 Hertz?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>A complex sinusoid <IMG
|
|
WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img669.png"
|
|
ALT="$X[n]$"> has frequency 11025 Hertz, amplitude
|
|
50 and initial phase 135 degrees. Another one, <IMG
|
|
WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img717.png"
|
|
ALT="$Y[n]$">, has the same frequency,
|
|
but amplitude 20 and initial phase 45 degrees. What are the amplitude and
|
|
initial phase of the sum of <IMG
|
|
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img670.png"
|
|
ALT="$X$"> and <IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img672.png"
|
|
ALT="$Y$">?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>What are the frequency, initial phase, and amplitude of the signal
|
|
obtained when <IMG
|
|
WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img669.png"
|
|
ALT="$X[n]$"> (above) is delayed 4 samples?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Show that the frequency response of
|
|
a recirculating comb filter with delay time <IMG
|
|
WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img28.png"
|
|
ALT="$d$"> and feedback gain <IMG
|
|
WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img29.png"
|
|
ALT="$g$">, as a
|
|
function of angular frequency <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img27.png"
|
|
ALT="$\omega $">, is equal to:
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
{[ {{(1-g \cos (\omega d))}^2} + {{(g \sin (\omega d))}^2} ]}
|
|
^
|
|
{-1/2}
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="246" HEIGHT="30" BORDER="0"
|
|
SRC="img851.png"
|
|
ALT="\begin{displaymath}
|
|
{[ {{(1-g \cos (\omega d))}^2} + {{(g \sin (\omega d))}^2} ]}
|
|
^
|
|
{-1/2}
|
|
\end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
|
|
<P>
|
|
</LI>
|
|
</OL>
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2427"
|
|
HREF="node127.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2421"
|
|
HREF="node104.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2417"
|
|
HREF="node125.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2423"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2425"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2428"
|
|
HREF="node127.html">Filters</A>
|
|
<B> Up:</B> <A ID="tex2html2422"
|
|
HREF="node104.html">Time shifts and delays</A>
|
|
<B> Previous:</B> <A ID="tex2html2418"
|
|
HREF="node125.html">Pitch shifter</A>
|
|
<B> <A ID="tex2html2424"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2426"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
|