2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
|
<!--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>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<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="node32.html">
|
|
|
|
|
<LINK REL="up" HREF="node26.html">
|
|
|
|
|
<LINK REL="next" HREF="node40.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1116"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node40.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1110"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node26.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1106"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node38.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1112"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1114"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html1117"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node40.html">Audio and control computations</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html1111"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node26.html">Wavetables and samplers</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html1107"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node38.html">Automatic read point precession</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html1113"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html1115"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<H1><A ID="SECTION00670000000000000000">
|
2022-04-12 21:54:18 -03:00
|
|
|
Exercises</A>
|
|
|
|
|
</H1>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
|
|
|
|
<OL>
|
|
|
|
|
<LI>If a wavetable with <IMG
|
|
|
|
|
WIDTH="35" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img296.png"
|
|
|
|
|
ALT="$1000$"> samples is played back at unit transposition,
|
|
|
|
|
at a sample rate of 44100 Hertz, how long does the resulting sound last?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>A one-second wavetable is played back in 0.5 seconds. By what
|
|
|
|
|
interval is the sound transposed?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>Still assuming a one-second wavetable, if we play it back periodically
|
|
|
|
|
(in a loop), at how many Hertz should we loop the wavetable to transpose the
|
|
|
|
|
original sound upward one half-step?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>We wish to play a wavetable (recorded at <IMG
|
|
|
|
|
WIDTH="76" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img297.png"
|
|
|
|
|
ALT="$R=44100$">), looping ten times
|
|
|
|
|
per second, so that the original sound stored in the wavetable is transposed up
|
|
|
|
|
a perfect fifth (see Page <A HREF="node14.html#r-intervals"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="crossref.png"></A>). How large a segment of the
|
2022-04-12 21:54:18 -03:00
|
|
|
wavetable, in samples, should be played back?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>Suppose you wish to use waveform stretching on a wavetable that holds a
|
|
|
|
|
periodic waveform of period 100. You wish to hear the untransposed spectrum at
|
|
|
|
|
a period of 200 samples. By what duty factor should you squeeze the waveform?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>The first half of a wavetable contains a cycle of a sinusoid of peak
|
|
|
|
|
amplitude one. The second half contains zeros. What is the strength of the
|
|
|
|
|
second partial of the wavetable?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>A sinusoid is stored in a wavetable with period 4 so that the first four
|
|
|
|
|
elements are 0, 1, 0, and -1, corresponding to indices 0, 1, 2, and 3. What
|
|
|
|
|
value do we get for an input of 1.5: (a) using 2-point interpolation? (b)
|
|
|
|
|
using 4-point interpolation? (c) What's the value of the original sinusoid
|
|
|
|
|
there?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
<LI>If a wavetable's contents all fall between -1 and 1 in value, what is the
|
|
|
|
|
range of possible outputs of wavetable lookup using 4-point interpolation?
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
</LI>
|
|
|
|
|
</OL>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1116"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node40.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1110"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node26.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1106"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node38.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1112"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html1114"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html1117"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node40.html">Audio and control computations</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html1111"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node26.html">Wavetables and samplers</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html1107"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node38.html">Automatic read point precession</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html1113"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html1115"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
