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<H2><A NAME="SECTION00951000000000000000">
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Ring modulation and spectra</A>
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</H2>
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<P>
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Example E01.spectrum.pd serves to introduce a spectrum
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measurement tool we'll be using; here we'll skip to the
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second example, E02.ring.modulation.pd, which shows the effect of ring modulating a harmonic
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spectrum (which was worked out theoretically in Section <A HREF="node77.html#sect5.ringmod">5.2</A> and
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shown in Figure <A HREF="node77.html#fig05.04">5.4</A>). In the example we consider a signal whose
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harmonics (from 0 through 5) all have unit amplitude. The harmonics may be
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turned on and off separately using toggle switches. When they are all on,
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the spectral envelope peaks at DC (because the constant signal counts twice as
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strongly as the other sinusoids), has a flat region from
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harmonics 1 through 5, and then descends to zero.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig05.09"></A><A NAME="5792"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.9:</STRONG>
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Ring modulation of a complex tone by a sinusoid: (a) its realization;
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(b) a measured spectrum.</CAPTION>
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<TR><TD><IMG
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WIDTH="444" HEIGHT="656" BORDER="0"
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ALT="\begin{figure}\psfig{file=figs/fig05.09.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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In the signal generation portion of the patch (part (a) of the figure), we sum
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the six partials and multiply the sum by the single, carrier oscillator.
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(The six signals are summed implicitly by connecting them all to the same
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inlet of the <TT>*~</TT> object.) The value of "fundamental" at the top
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is computed to line up well with the spectral analysis, whose result is
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shown in part (b) of the figure.
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<P>
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The spectral analysis (which uses techniques that won't be described until
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Chapter <A HREF="node163.html#chapter-fourier">9</A>) shows the location of the
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sinusoids (assuming a discrete spectrum) on the horizontal axis and their
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magnitudes on the vertical one. So the presence of a peak at DC of magnitude
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one in the spectrum of the input signal predicts, à la Figure <A HREF="node77.html#fig05.03">5.3</A>,
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that there should be a peak in the output spectrum, at the carrier frequency,
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of height 1/2. Similarly, the two other sinusoids in the input signal, which
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have height 1/2 in the spectrum, give rise to two peaks each, of height 1/4,
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in the output. One of these four has been reflected about the left edge of
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the figure (taking the absolute value of its negative frequency).
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