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HREF="node122.html">Non-recirculating comb filter as</A>
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html2388"
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<H2><A ID="SECTION0011107000000000000000">
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Time-varying complex comb filter: shakers</A>
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</H2>
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<P>
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Example G07.shaker.pd (Figure <A HREF="#fig07.30">7.30</A>) shows a different way of extending the
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idea of a comb filter. Here we combine the input signal at four different
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time shifts (instead of two, as in the original non-recirculating comb filter),
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each at a different positive or negative gain. To do this, we insert the
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input signal into a delay line and tap it at three different points; the
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fourth "tap" is the original, un-delayed signal.
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<P>
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<DIV ALIGN="CENTER"><A ID="fig07.30"></A><A ID="8287"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7.30:</STRONG>
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A "shaker", a four-tap comb filter with randomly varying gains
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on the taps.</CAPTION>
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<TR><TD><IMG
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WIDTH="591" HEIGHT="386" BORDER="0"
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SRC="img845.png"
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ALT="\begin{figure}\psfig{file=figs/fig07.30.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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As a way of thinking about the frequency response of a four-tap comb filter,
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we consider first what happens when two of the four gains are close to zero.
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Then we end up with a simple non-recirculating comb filter, with the slight
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complication that the gains of the two delayed copies may be different. If they
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are both of the same sign, we get the same peaks and valleys as predicted
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in Section <A HREF="node108.html#sect7.network">7.3</A>, only with the valleys between peaks possibly
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more shallow. If they are opposite in sign, the valleys become peaks and
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the peaks become valleys.
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<P>
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Depending on which two taps we supposed were nonzero, the peaks and valleys are
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spaced by different amounts; the delay times are chosen so that 6 different
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delay times can arise in this way, ranging between 6 and 30 milliseconds. In
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the general case in which all the gains are non-zero, we can imagine the
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frequency response function varying continuously between these extremes, giving
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a succession of complicated patterns. This has the effect of raising and
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lowering the amplitudes of the partials of the incoming signal, all
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independently of the others, in a complicated pattern, to give a steadily
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time-varying timbre.
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<P>
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The right-hand side of the patch takes care of changing the gains of the
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input signal and its three time-shifted copies. Each time the <TT>metro</TT> object
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fires, a counter is incremented (the <TT>f</TT>, <TT>+ 1</TT>, and
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<TT>mod 4</TT> objects). This controls which of the amplitudes will be changed.
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The amplitude itself is computed by making a random number and normalizing it to
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lie between -0.7 and 1.3 in value. The random value and the index are packed
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(along with a third value, a time interval) and this triple goes to the
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<TT>route</TT> object. The first element of the triple (the
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counter) selects which output to send the other two values to; as a result,
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one of the four possible <TT>line~</TT> objects gets a message to ramp to
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a new value.
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<P>
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If the time variation is done quickly enough, there is also a modulation
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effect on the original signal; in this situation the straight line segments
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used in this example should be replaced by modulating signals with more
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controllable frequency content, for instance using filters (the
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subject of Chapter 8).
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