<!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="node18.html">
<LINK REL="up" HREF="node7.html">
<LINK REL="next" HREF="node26.html">
</HEAD>

<BODY >
<!--Navigation Panel-->
<A ID="tex2html905"
  HREF="node26.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
 SRC="next.png"></A> 
<A ID="tex2html899"
  HREF="node7.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
 SRC="up.png"></A> 
<A ID="tex2html895"
  HREF="node24.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
 SRC="prev.png"></A> 
<A ID="tex2html901"
  HREF="node4.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
 SRC="contents.png"></A> 
<A ID="tex2html903"
  HREF="node201.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
 SRC="index.png"></A> 
<BR>
<B> Next:</B> <A ID="tex2html906"
  HREF="node26.html">Wavetables and samplers</A>
<B> Up:</B> <A ID="tex2html900"
  HREF="node7.html">Sinusoids, amplitude and frequency</A>
<B> Previous:</B> <A ID="tex2html896"
  HREF="node24.html">More additive synthesis</A>
 &nbsp; <B>  <A ID="tex2html902"
  HREF="node4.html">Contents</A></B> 
 &nbsp; <B>  <A ID="tex2html904"
  HREF="node201.html">Index</A></B> 
<BR>
<BR>
<!--End of Navigation Panel-->

<H1><A ID="SECTION005100000000000000000">
Exercises</A>
</H1>

<P>

<OL>
<LI>A sinusoid (Page <A HREF="node7.html#eq-realsinusoid"><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]"
 SRC="crossref.png"></A>) has initial phase <IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img162.png"
 ALT="$\phi=0$"> and 
angular frequency <!-- MATH
 $\omega = \pi/10$
 -->
<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img163.png"
 ALT="$\omega = \pi/10$">.  What is its period in samples?  What is
the phase at sample number <IMG
 WIDTH="50" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img164.png"
 ALT="$n=10$">?

<P>
</LI>
<LI>Two sinusoids have periods of 20 and 30 samples, respectively.  What is
the period of the sum of the two?

<P>
</LI>
<LI>If 0 dB corresponds to an amplitude of 1,
how many dB corresponds to amplitudes of 1.5, 2, 3, and 5?

<P>
</LI>
<LI>Two uncorrelated signals of RMS amplitude 3 and 4 are added; what's the
RMS amplitude of the sum?

<P>
</LI>
<LI>How many uncorrelated signals, all of equal amplitude, would you have
to add to get a signal that is 9 dB greater in amplitude?

<P>
</LI>
<LI>What is the angular frequency of middle C at 44100 samples per second?

<P>
</LI>
<LI>Two sinusoids play at middle C (MIDI 60) and the neighboring C sharp
(MIDI 61).  What is the difference, in Hertz, between their frequencies?

<P>
</LI>
<LI>How many cents is the interval between the seventh and the eighth harmonic of
a periodic signal?

<P>
</LI>
<LI>If an audio signal <!-- MATH
 $x[n], n = 0, ..., N-1$
 -->
<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img165.png"
 ALT="$x[n], n = 0, ..., N-1$"> has peak amplitude 1, what
is the minimum possible RMS amplitude? What is the maximum possible?

<P>
</LI>
</OL>
<HR>
<!--Navigation Panel-->
<A ID="tex2html905"
  HREF="node26.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
 SRC="next.png"></A> 
<A ID="tex2html899"
  HREF="node7.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
 SRC="up.png"></A> 
<A ID="tex2html895"
  HREF="node24.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
 SRC="prev.png"></A> 
<A ID="tex2html901"
  HREF="node4.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
 SRC="contents.png"></A> 
<A ID="tex2html903"
  HREF="node201.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
 SRC="index.png"></A> 
<BR>
<B> Next:</B> <A ID="tex2html906"
  HREF="node26.html">Wavetables and samplers</A>
<B> Up:</B> <A ID="tex2html900"
  HREF="node7.html">Sinusoids, amplitude and frequency</A>
<B> Previous:</B> <A ID="tex2html896"
  HREF="node24.html">More additive synthesis</A>
 &nbsp; <B>  <A ID="tex2html902"
  HREF="node4.html">Contents</A></B> 
 &nbsp; <B>  <A ID="tex2html904"
  HREF="node201.html">Index</A></B> 
<!--End of Navigation Panel-->
<ADDRESS>
Miller Puckette
2006-12-30
</ADDRESS>
</BODY>
</HTML>