179 lines
5.3 KiB
HTML
179 lines
5.3 KiB
HTML
<!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="node50.html">
|
|
<LINK REL="up" HREF="node40.html">
|
|
<LINK REL="next" HREF="node58.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html1387"
|
|
HREF="node58.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A NAME="tex2html1381"
|
|
HREF="node40.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A NAME="tex2html1377"
|
|
HREF="node56.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A NAME="tex2html1383"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A NAME="tex2html1385"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html1388"
|
|
HREF="node58.html">Automation and voice management</A>
|
|
<B> Up:</B> <A NAME="tex2html1382"
|
|
HREF="node40.html">Audio and control computations</A>
|
|
<B> Previous:</B> <A NAME="tex2html1378"
|
|
HREF="node56.html">MIDI-style synthesizer</A>
|
|
<B> <A NAME="tex2html1384"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A NAME="tex2html1386"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H1><A NAME="SECTION007110000000000000000">
|
|
Exercises</A>
|
|
</H1>
|
|
|
|
<P>
|
|
|
|
<OL>
|
|
<LI>How many partials of a tone at A 440 can be represented digitally at a
|
|
sample rate of 44100 Hertz?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>What frequency would you hear if you synthesized a sinusoid at 88000 Hertz
|
|
at a sample rate of 44100?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Suppose you are synthesizing sound at 44100 Hertz, and are computing
|
|
64-sample audio blocks. A control event is scheduled to happen at an elapsed
|
|
time of exactly one second, using the fast-as-possible update scheme. At what
|
|
sample does the update actually occur?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Sampling at 44100, we wish to approximately play a tone at middle C by
|
|
repeating a fixed waveform every N samples. What value of <IMG
|
|
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img3.png"
|
|
ALT="$N$"> should we
|
|
choose, and how many cents (Page <A HREF="node11.html#eq-pitchmidi"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
|
|
SRC="crossref.png"></A>) are we off from the
|
|
``true" middle C?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Two sawtooth waves, of unit amplitude, have frequencies 200 and 300 Hertz,
|
|
respectively. What is the periodicity of the sum of the two? What if you
|
|
then wrapped the sum back to the range from 0 to 1? Does this result change
|
|
depending on the relative phase of the two?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Two sawtooth waves, of equal frequency and amplitude and one half cycle
|
|
out of phase, are summed. What is the waveform of the sum, and what are its
|
|
amplitude and frequency?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>What is the relative level, in decibels, of a sawtooth wave's third
|
|
harmonic (three times the fundamental) compared to that of the fundamental?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Suppose you synthesize a 44000-Hertz sawtooth wave at a sample rate
|
|
of 44100 Hertz. What is the resulting waveform?
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Using the techniques of Section <A HREF="node47.html#sect3.analog">3.7</A>, draw a block diagram
|
|
for generating two phase-locked sinusoids at 500 and 700 Hertz.
|
|
|
|
<P>
|
|
</LI>
|
|
<LI>Draw a block diagram showing how to use thresholding to detect when one
|
|
audio signal exceeds another one in value. (You might want to do this to
|
|
detect and filter out feedback from speakers to microphones.)
|
|
|
|
<P>
|
|
</LI>
|
|
</OL>
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html1387"
|
|
HREF="node58.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A NAME="tex2html1381"
|
|
HREF="node40.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A NAME="tex2html1377"
|
|
HREF="node56.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A NAME="tex2html1383"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A NAME="tex2html1385"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html1388"
|
|
HREF="node58.html">Automation and voice management</A>
|
|
<B> Up:</B> <A NAME="tex2html1382"
|
|
HREF="node40.html">Audio and control computations</A>
|
|
<B> Previous:</B> <A NAME="tex2html1378"
|
|
HREF="node56.html">MIDI-style synthesizer</A>
|
|
<B> <A NAME="tex2html1384"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A NAME="tex2html1386"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|