167 lines
6.2 KiB
HTML
167 lines
6.2 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>Phase bashing</TITLE>
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<B> Next:</B> <A NAME="tex2html3214"
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HREF="node178.html">Examples</A>
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<B> Up:</B> <A NAME="tex2html3208"
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HREF="node163.html">Fourier analysis and resynthesis</A>
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<B> Previous:</B> <A NAME="tex2html3202"
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HREF="node176.html">Phase relationships between channels</A>
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<B> <A NAME="tex2html3210"
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HREF="node4.html">Contents</A></B>
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HREF="node201.html">Index</A></B>
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<BR>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION001360000000000000000"></A>
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<A NAME="sect9-bash"></A>
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<BR>
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Phase bashing
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</H1>
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<P>
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In Section <A HREF="node29.html#sect2.enveloping">2.3</A> on enveloped sampling we saw how to make a
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periodic waveform from a recorded sound, thereby borrowing the timbre of the
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original sound but playing it at a specified pitch. If the window into the
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recorded sound is made to precess in time, the resulting timbre varies
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in imitation of the recorded sound.
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<P>
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One important problem arises, which is that if we take waveforms from different
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windows of a sample (or from different samples), there is no guarantee that the
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phases of the two match up. If they don't the result can be ugly, since the
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random phase changes are heard as frequency fluctuations. This can be
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corrected using Fourier analysis and resynthesis [<A
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HREF="node202.html#r-puckette05">Puc05</A>].
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig09.13"></A><A NAME="12680"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 9.13:</STRONG>
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Phase-bashing a recorded sound (here, a sinusoid with rising
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frequency) to give a series of oscillator wavetables.</CAPTION>
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<TR><TD><IMG
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WIDTH="382" HEIGHT="401" BORDER="0"
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SRC="img1212.png"
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ALT="\begin{figure}\psfig{file=figs/fig09.13.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Figure <A HREF="#fig09.13">9.13</A> shows a simple way to use Fourier analysis to align
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phases in a series of windows in a recording. We simply take the FFT of the
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window and then set each phase to zero for even values of <IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img58.png"
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ALT="$k$"> and
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<IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img41.png"
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ALT="$\pi $"> for odd ones. The phase at the center of the window is thus zero for
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both even and odd values of <IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img58.png"
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ALT="$k$">. To set the phases (the arguments of the
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complex amplitudes in the spectrum) in the desired way, first we find the
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magnitude, which can be considered a complex number with argument zero. Then
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multiplying by <IMG
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WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
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SRC="img1213.png"
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ALT="$(-1)^k$"> adjusts the amplitude so that it is positive and
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negative in alternation. Then we take the inverse Fourier transform, without
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even bothering to window again on the way back; we will probably want to apply
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a windowing envelope later anyway as was shown in Figure <A HREF="node29.html#fig02.07">2.7</A>. The
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results can be combined with the modulation techniques of Chapter 6 to yield
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powerful tools for vocal and other imitative synthesis.
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<P>
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<HR>
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HREF="node201.html">
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<BR>
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<B> Next:</B> <A NAME="tex2html3214"
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HREF="node178.html">Examples</A>
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<B> Up:</B> <A NAME="tex2html3208"
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HREF="node163.html">Fourier analysis and resynthesis</A>
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<B> Previous:</B> <A NAME="tex2html3202"
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HREF="node176.html">Phase relationships between channels</A>
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<B> <A NAME="tex2html3210"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html3212"
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HREF="node201.html">Index</A></B>
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<!--End of Navigation Panel-->
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<ADDRESS>
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Miller Puckette
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2006-12-30
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</ADDRESS>
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</HTML>
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