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Ring ModulationRing modulation is an audio effect performed by multiplying two audio signals, where one is typically a sine-wave or another simple waveform. It is referred to as "ring" modulation because the analog circuit of diodes originally used to implement this effect took the shape of a ring. Ring modulators are mostly used in synthesizers. They combine or heterodyne two waveforms, and output the sum and difference between the two. This process of ring modulation, also called amplitude modulation, produces a signal rich in overtones, suitable for producing bell-like or otherwise metallic sounds. Ring modulators were used by the BBC Radiophonic Workshop to produce the distinctive voice of the Daleks in the television series Doctor Who. Modern ring modulators are implemented using digital signal processing techniques by simply multiplying the time domain signals. Multiplication in the time domain is the same as convolution in the frequency domain, so the output waveform contains the sum and difference of the input frequencies. Thus, in the basic case where two sine waves of frequencies f1 and f2 (f2>f1) are multiplied, two new sine waves are created, with one at f1+f2 and the other at f2-f1. Two points to note are that firstly the two new waves are unlikely to be harmonically related and secondly that (in a well designed ring modulator) the original signals are not present. It is this that gives the ring modulator its unique tones. Interesting harmonics can be generated by carefully selecting and changing the frequency of the two input waveforms. If the signals are wideband, it is likely that the circular convolution will cause aliasing distortion, so it is common to oversample the operation or filter the signals prior to ring modulation. On the C64 SID chip, ring modulation multiplies a triangle wave with a square wave. A ring modulator module was a common feature on early modular Moog synthesizers. The ring modulator went out of fashion with the advent of all-in-one synthesizers and sampled-based synthesizers, but has returned as a feature in digital modelling and software synthesizers. See also: Heterodyne External link
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