Ring modulation and spectra

The first Pd example for this chapter, E01.spectrum.pd, serves to introduce a spectrum measurement tool we'll use often. We'll start with the second example, E02.ring.modulation.pd, which shows the effect of ring modulating a harmonic spectrum (which is worked out theoretically in section 5.2 and shown in Figure 5.4). In the example we consider a signal whose harmonics (from 0 through 5) all have unit amplitude. Because signals of frequency 0 count twice as heavily (per peak amplitude) as nonzero-frequency sinusoids do, the spectral envelope peaks at DC, has a flat region from harmonics 1 through 5, and then descends to zero.

Figure 5.9: Ring modulation of a complex tone by a sinusoid: (a) its realization; (b) a measured spectrum

In the signal generation portion of the patch (part (a) of the figure), we sum the six partials and multiply the sum by the single, modulating oscillator. (The six signals are summed implicitly by connecting them all to the same inlet of the *~ object.) The value of ``fundamental" at the top is computed to line up well with the spectral analysis, whose result is shown in part (b) of the figure.

The spectral analysis is done using techniques which won't be described until chapter , but in sum, the output shows the location of the sinusoids (assuming a discrete spectrum) on the horizontal axis and their magnitudes on the vertical one. So the presence of a peak at DC of magnitude one in the spectrum of the input signal predicts, ala figure 5.3, that there should be a peak in the output spectrum, at the modulating frequency, of height 1/2. Similarly, the two other sinusoids in the input signal, which have height 1/2 in the spectrum, give rise to two peaks each, of height 1/4, in the output. One of these four has been reflected about the left edge of the figure (the $f=0$ axis.)