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<H2><A ID="SECTION001372000000000000000">
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Narrow-band companding: noise suppression</A>
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</H2>
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<P>
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<DIV ALIGN="CENTER"><A ID="fig09.16"></A><A ID="12719"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 9.16:</STRONG>
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Noise suppression as an example of narrow-band companding: (a)
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analysis and reconstruction of the signal; (b) computation of the
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"mask".</CAPTION>
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<TR><TD><IMG
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WIDTH="663" HEIGHT="477" BORDER="0"
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SRC="img1227.png"
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ALT="\begin{figure}\psfig{file=figs/fig09.16.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Example I04.noisegate.pd (Figure <A HREF="#fig09.16">9.16</A>) shows an example of narrow-band
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companding using Fourier analysis/resynthesis. (This is a realization of the
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block diagram of Figure <A HREF="node173.html#fig09.08">9.8</A>.) Part (a) of the figure shows a filter
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configuration similar to the previous example, except that the gain for each
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channel is now a function of the channel magnitude.
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<P>
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For each <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="$k$">, if we let <IMG
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WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1228.png"
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ALT="$s[k]$"> denote the power in channel <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 let
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<IMG
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WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1229.png"
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ALT="$m[k]$"> be a mask level (a level presumably somewhat higher than the noise
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power for channel <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="$k$">), then the gain in channel <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="$k$"> is given by
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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\left \{
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\begin{array}{ll}
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{\sqrt{{s[k]-m[k]}\over {s[k]}}} & {s[k] > m[k]} \\
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0 & \mbox{otherwise}
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\end{array}
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\right .
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\end{displaymath}
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-->
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<IMG
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WIDTH="186" HEIGHT="55" BORDER="0"
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SRC="img1230.png"
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ALT="\begin{displaymath}
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\left \{
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\begin{array}{ll}
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{\sqrt{{s[k]-m[k]}\over {s[k]}...
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... {s[k] > m[k]} \\
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0 & \mbox{otherwise}
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\end{array} \right .
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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The power in the <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="$k$">th channel is thus reduced by <IMG
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WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1229.png"
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ALT="$m[k]$"> if possible,
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and otherwise replaced by zero.
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<P>
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The mask itself is the product of the measured average noise in each channel,
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which is contained in the table "$0-mask", multiplied by a value named
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"mask-level". The average noise is measured in a subpatch
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(<TT>pd calculate-mask</TT>), whose contents are shown in part (b) of the
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figure. To compute the mask we are using two new new objects:
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<P>
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<BR><!-- MATH
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$\fbox{\texttt{bang\~}}$
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-->
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<IMG
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WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1231.png"
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ALT="\fbox{\texttt{bang\~}}">:
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<A ID="12903"></A>send a bang in advance of each block of computation. The bang appears at the
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logical time of the first sample in each block (the earliest logical time whose
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control computation affects that block and not the previous one), following
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the scheme shown
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in Figure <A HREF="node42.html#fig03.02">3.2</A>.
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<P>
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<BR><!-- MATH
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$\fbox{\texttt{tabsend\~}}$
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-->
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<IMG
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WIDTH="81" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img1233.png"
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ALT="\fbox{\texttt{tabsend\~}}">:
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<A ID="12904"></A>the companion object for <TT>tabreceive~</TT>, repeatedly copies its input to
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the contents of a table, affecting up to the first <IMG
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WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img3.png"
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ALT="$N$"> samples of the table.
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<P>
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The power averaging process is begun by sending a time duration in milliseconds
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to "make-mask". The patch computes the equivalent number of blocks <IMG
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WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img21.png"
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ALT="$b$">
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and generates a sequence of weights: <!-- MATH
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$1, 1/2, 1/3, \ldots, 1/b$
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-->
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<IMG
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WIDTH="131" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1235.png"
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ALT="$1, 1/2, 1/3, \ldots, 1/b$">,
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by which each of the <IMG
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WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img21.png"
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ALT="$b$"> following blocks' power is averaged into whatever the
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mask table held at the previous block. At the end of <IMG
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WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img21.png"
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ALT="$b$"> blocks the table holds
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the equally-weighted average of all <IMG
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WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img21.png"
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ALT="$b$"> power measurements. Thereafter, the
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weight for averaging new power measurements is zero, so the measured average
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stops evolving.
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<P>
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To use this patch for classical noise suppression requires at least a few
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seconds of recorded noise without the "signal" present. This is played into
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the patch, and its duration sent to "make-mask", so that the
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"$0-mask" table holds the average measured noise power for each channel.
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Then, making the assumption that the noisy part of the signal rarely exceeds 10
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times its average power (for example), "mask-level" is set to 10, and the
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signal to be noise-suppressed is sent through part (a) of the patch. The noise
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will be almost all gone, but those channels in which the signal exceeds 20
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times the noise power will only be attenuated by 3dB, and higher-power channels
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progressively less. (Of course, actual noise suppression might not be the
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most interesting application of the patch; one could try masking any signal
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from any other one.)
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<P>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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