171 lines
5.3 KiB
HTML
171 lines
5.3 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
||
|
|
|
||
|
|
<!--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>
|
||
|
|
<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="node80.html">
|
||
|
|
<LINK REL="up" HREF="node75.html">
|
||
|
|
<LINK REL="next" HREF="node89.html">
|
||
|
|
</HEAD>
|
||
|
|
|
||
|
|
<BODY >
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html1854"
|
||
|
|
HREF="node89.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html1848"
|
||
|
|
HREF="node75.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html1844"
|
||
|
|
HREF="node87.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html1850"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html1852"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html1855"
|
||
|
|
HREF="node89.html">Designer spectra</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html1849"
|
||
|
|
HREF="node75.html">Modulation</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html1845"
|
||
|
|
HREF="node87.html">Phase modulation and FM</A>
|
||
|
|
<B> <A NAME="tex2html1851"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html1853"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<BR>
|
||
|
|
<BR>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
|
||
|
|
<H1><A NAME="SECTION00960000000000000000">
|
||
|
|
Exercises</A>
|
||
|
|
</H1>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
|
||
|
|
<OL>
|
||
|
|
<LI>A sound has fundamental 440. How could it be ring modulated to
|
||
|
|
give a tone at 110 Hertz with only odd partials? How could you then fill in the
|
||
|
|
even ones if you wanted to?
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
<LI>A sinusoid with frequency 400 and unit peak amplitude is squared. What
|
||
|
|
are the amplitudes and frequencies of the new signal's components?
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
<LI>What carrier and modulation frequencies would you give a two-operator FM
|
||
|
|
instrument to give frequencies of 618, 1000, and 2618 Hertz? (This is
|
||
|
|
a prominent feature of Chowning's <I>Stria</I> [<A
|
||
|
|
HREF="node202.html#r-dodge85">DJ85</A>].)
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
<LI>Two sinusoids with frequency 300 and 400 Hertz and peak amplitude
|
||
|
|
one (so RMS amplitude <IMG
|
||
|
|
WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||
|
|
SRC="img549.png"
|
||
|
|
ALT="$\approx$">0.707) are multiplied. What is the RMS
|
||
|
|
amplitude of the product?
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
<LI>Suppose you wanted to make FM yet more complicated by modulating the
|
||
|
|
<I>modulating</I> oscillator, as in:
|
||
|
|
<BR><P></P>
|
||
|
|
<DIV ALIGN="CENTER">
|
||
|
|
<!-- MATH
|
||
|
|
\begin{displaymath}
|
||
|
|
\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
|
||
|
|
\end{displaymath}
|
||
|
|
-->
|
||
|
|
|
||
|
|
<IMG
|
||
|
|
WIDTH="243" HEIGHT="29" BORDER="0"
|
||
|
|
SRC="img550.png"
|
||
|
|
ALT="\begin{displaymath}
|
||
|
|
\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
|
||
|
|
\end{displaymath}">
|
||
|
|
</DIV>
|
||
|
|
<BR CLEAR="ALL">
|
||
|
|
<P></P>
|
||
|
|
How, qualitatively speaking, would the spectrum differ from that of the simple
|
||
|
|
two-modulator example (Section <A HREF="node87.html#sect5.example.fm">5.5</A>)?
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
<LI>A sinusoid at a frequency <IMG
|
||
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
||
|
|
SRC="img27.png"
|
||
|
|
ALT="$\omega $"> is ring modulated by another
|
||
|
|
sinusoid at exactly the same frequency. At what phase differences will the
|
||
|
|
DC component of the result disappear?
|
||
|
|
|
||
|
|
<P>
|
||
|
|
</LI>
|
||
|
|
</OL>
|
||
|
|
<HR>
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html1854"
|
||
|
|
HREF="node89.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html1848"
|
||
|
|
HREF="node75.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html1844"
|
||
|
|
HREF="node87.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html1850"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html1852"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html1855"
|
||
|
|
HREF="node89.html">Designer spectra</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html1849"
|
||
|
|
HREF="node75.html">Modulation</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html1845"
|
||
|
|
HREF="node87.html">Phase modulation and FM</A>
|
||
|
|
<B> <A NAME="tex2html1851"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html1853"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
<ADDRESS>
|
||
|
|
Miller Puckette
|
||
|
|
2006-12-30
|
||
|
|
</ADDRESS>
|
||
|
|
</BODY>
|
||
|
|
</HTML>
|