170 lines
6.3 KiB
HTML
170 lines
6.3 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>Strategies for band-limiting sawtooth waves</TITLE>
|
|
<META NAME="description" CONTENT="Strategies for band-limiting sawtooth waves">
|
|
<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="node198.html">
|
|
<LINK REL="up" HREF="node197.html">
|
|
<LINK REL="next" HREF="node200.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html3539"
|
|
HREF="node200.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html3533"
|
|
HREF="node197.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html3529"
|
|
HREF="node198.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html3535"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html3537"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html3540"
|
|
HREF="node200.html">Exercises</A>
|
|
<B> Up:</B> <A ID="tex2html3534"
|
|
HREF="node197.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html3530"
|
|
HREF="node198.html">Combining sawtooth waves</A>
|
|
<B> <A ID="tex2html3536"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html3538"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A ID="SECTION001452000000000000000">
|
|
Strategies for band-limiting sawtooth waves</A>
|
|
</H2>
|
|
|
|
<P>
|
|
|
|
<DIV ALIGN="CENTER"><A ID="fig10.14"></A><A ID="14512"></A>
|
|
<TABLE>
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 10.14:</STRONG>
|
|
Alternative techniques for making waveforms with corners: (a) a
|
|
triangle wave as the minimum of two line segments; (b) clipping a triangle wave to
|
|
make an "envelope".</CAPTION>
|
|
<TR><TD><IMG
|
|
WIDTH="617" HEIGHT="359" BORDER="0"
|
|
SRC="img1377.png"
|
|
ALT="\begin{figure}\psfig{file=figs/fig10.14.ps}\end{figure}"></TD></TR>
|
|
</TABLE>
|
|
</DIV>
|
|
|
|
<P>
|
|
Example J05.triangle.pd (Figure <A HREF="#fig10.14">10.14</A>, part a) shows a simple way to make a
|
|
triangle wave, in which only the slope of the rising and falling segment are
|
|
specified. A phasor supplies the rising shape (its amplitude being the slope),
|
|
and the same phasor, subtracted from one, gives the decaying shape. The
|
|
minimum of the two linear functions follows the rising phasor up to the
|
|
intersection of the two, and then follows the falling phasor back down to zero
|
|
at the end of the cycle.
|
|
|
|
<P>
|
|
A triangle wave can be clipped above and below to make a trapezoidal wave,
|
|
which can be used either as an audio-frequency pulse or, at a lower fundamental
|
|
frequency, as a repeating ASR (attack/sustain/release) envelope. Patch
|
|
J06.enveloping.pd (Figure <A HREF="#fig10.14">10.14</A> part b) demonstrates this. The same rising
|
|
shape is used as in the previous example, and the falling shape differs only
|
|
in that its phase is set so that it falls to zero at a controllable point (not
|
|
necessarily at the end of the cycle as before). The <TT>clip~</TT> object prevents
|
|
it from rising above 1 (so that, if the intersection of the two segments is
|
|
higher than one, we get a horizontal "sustain" segment), and also from falling
|
|
below zero, so that once the falling shape reaches zero, the output is zero for
|
|
the rest of the cycle.
|
|
|
|
<P>
|
|
Example J07.oversampling.pd shows how to use up-sampling to reduce foldover when using a
|
|
<TT>phasor~</TT> object as an audio sawtooth wave. A subpatch, running at 16
|
|
times the base sample rate, contains the <TT>phasor~</TT> object and a
|
|
three-pole, three-zero Butterworth filter to reduce the amplitudes of partials
|
|
above the Nyquist frequency of the parent patch (running at the original sample
|
|
rate) so that the output won't fold over when it is down-sampled at the
|
|
<TT>outlet~</TT> object. Example J08.classicsynth.pd demonstrates using up-sampled
|
|
phasors as signal generators to make an imitation of a classic synthesizer
|
|
doing subtractive synthesis.
|
|
|
|
<P>
|
|
Example J09.bandlimited.pd shows how to use transition splicing as an alternative way to
|
|
generate a sawtooth wave with controllable foldover. This has the advantage of
|
|
being more direct (and usually less compute-intensive) than the up-sampling
|
|
method. On the other hand, this technique depends on using the reciprocal of
|
|
the fundamental frequency as an audio signal in its own right (to control the
|
|
amplitude of the sweeping signal that reads the transition table) and, in the
|
|
same way as for the PAF technique of Chapter <A HREF="node89.html#chapter-paf">6</A>, care must be
|
|
taken to avoid clicks if the fundamental frequency changes discontinuously.
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html3539"
|
|
HREF="node200.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html3533"
|
|
HREF="node197.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html3529"
|
|
HREF="node198.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html3535"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html3537"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html3540"
|
|
HREF="node200.html">Exercises</A>
|
|
<B> Up:</B> <A ID="tex2html3534"
|
|
HREF="node197.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html3530"
|
|
HREF="node198.html">Combining sawtooth waves</A>
|
|
<B> <A ID="tex2html3536"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html3538"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|