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>Phase bashing</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Phase bashing">
|
|
|
|
|
<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="next" HREF="node178.html">
|
|
|
|
|
<LINK REL="previous" HREF="node175.html">
|
|
|
|
|
<LINK REL="up" HREF="node163.html">
|
|
|
|
|
<LINK REL="next" HREF="node178.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html3213"
|
|
|
|
|
HREF="node178.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3207"
|
|
|
|
|
HREF="node163.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3201"
|
|
|
|
|
HREF="node176.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3209"
|
|
|
|
|
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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3211"
|
|
|
|
|
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>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html3214"
|
|
|
|
|
HREF="node178.html">Examples</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html3208"
|
|
|
|
|
HREF="node163.html">Fourier analysis and resynthesis</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html3202"
|
|
|
|
|
HREF="node176.html">Phase relationships between channels</A>
|
|
|
|
|
<B> <A NAME="tex2html3210"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html3212"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
<H1><A NAME="SECTION001360000000000000000"></A>
|
|
|
|
|
<A NAME="sect9-bash"></A>
|
|
|
|
|
<BR>
|
|
|
|
|
Phase bashing
|
|
|
|
|
</H1>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
In Section <A HREF="node29.html#sect2.enveloping">2.3</A> on enveloped sampling we saw how to make a
|
|
|
|
|
periodic waveform from a recorded sound, thereby borrowing the timbre of the
|
|
|
|
|
original sound but playing it at a specified pitch. If the window into the
|
|
|
|
|
recorded sound is made to precess in time, the resulting timbre varies
|
|
|
|
|
in imitation of the recorded sound.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
One important problem arises, which is that if we take waveforms from different
|
|
|
|
|
windows of a sample (or from different samples), there is no guarantee that the
|
|
|
|
|
phases of the two match up. If they don't the result can be ugly, since the
|
|
|
|
|
random phase changes are heard as frequency fluctuations. This can be
|
|
|
|
|
corrected using Fourier analysis and resynthesis [<A
|
|
|
|
|
HREF="node202.html#r-puckette05">Puc05</A>].
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
|
|
|
|
<DIV ALIGN="CENTER"><A NAME="fig09.13"></A><A NAME="12680"></A>
|
|
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 9.13:</STRONG>
|
|
|
|
|
Phase-bashing a recorded sound (here, a sinusoid with rising
|
|
|
|
|
frequency) to give a series of oscillator wavetables.</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="382" HEIGHT="401" BORDER="0"
|
|
|
|
|
SRC="img1212.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig09.13.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Figure <A HREF="#fig09.13">9.13</A> shows a simple way to use Fourier analysis to align
|
|
|
|
|
phases in a series of windows in a recording. We simply take the FFT of the
|
|
|
|
|
window and then set each phase to zero for even values of <IMG
|
|
|
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img58.png"
|
|
|
|
|
ALT="$k$"> and
|
|
|
|
|
<IMG
|
|
|
|
|
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img41.png"
|
|
|
|
|
ALT="$\pi $"> for odd ones. The phase at the center of the window is thus zero for
|
|
|
|
|
both even and odd values of <IMG
|
|
|
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img58.png"
|
|
|
|
|
ALT="$k$">. To set the phases (the arguments of the
|
|
|
|
|
complex amplitudes in the spectrum) in the desired way, first we find the
|
|
|
|
|
magnitude, which can be considered a complex number with argument zero. Then
|
|
|
|
|
multiplying by <IMG
|
|
|
|
|
WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img1213.png"
|
|
|
|
|
ALT="$(-1)^k$"> adjusts the amplitude so that it is positive and
|
|
|
|
|
negative in alternation. Then we take the inverse Fourier transform, without
|
|
|
|
|
even bothering to window again on the way back; we will probably want to apply
|
|
|
|
|
a windowing envelope later anyway as was shown in Figure <A HREF="node29.html#fig02.07">2.7</A>. The
|
|
|
|
|
results can be combined with the modulation techniques of Chapter 6 to yield
|
|
|
|
|
powerful tools for vocal and other imitative synthesis.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html3213"
|
|
|
|
|
HREF="node178.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3207"
|
|
|
|
|
HREF="node163.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3201"
|
|
|
|
|
HREF="node176.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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3209"
|
|
|
|
|
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 21:54:18 -03:00
|
|
|
<A NAME="tex2html3211"
|
|
|
|
|
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>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html3214"
|
|
|
|
|
HREF="node178.html">Examples</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html3208"
|
|
|
|
|
HREF="node163.html">Fourier analysis and resynthesis</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html3202"
|
|
|
|
|
HREF="node176.html">Phase relationships between channels</A>
|
|
|
|
|
<B> <A NAME="tex2html3210"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html3212"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
