- Ring modulation can also be achieved by multiplying two signals together, as will be shown in the following section on complex exponential signals. The result is a spectrum composed of the sum and difference frequencies of the two waveforms.
- If there are
*p*frequency components in one waveform and*q*frequency components in a second waveform, as many as 2*p q*components will be present in the spectrum of the waveform produced by multiplication of the two. - By carefully selecting the relationship between carrier and modulating frequencies, interesting and rich spectra can be produced via a relatively inexpensive computational operation.

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