# Ring modulation Audio: ring modulation (0:04)

ring modulation plays four sounds in succession and the ring modulation figure shows their waveforms:

1. The first sound, the top waveform, is a 200Hz sine wave.
2. The second sound, the middle waveform, is a 500Hz sine wave.
3. The third sound, the bottom waveform, contains two frequencies, 300Hz and 700Hz formed by ring modulating the first two sounds.
4. The fourth sound (waveform not shown) is ring modulated speech.

Ring Modulation (RM) is achieved by multiplying two sounds together.

Despite its formidable name RM is the simplest form of modulation and is easy to write.

Simple RM multiplies two sine waves together. The result is a single sound containing two frequencies known as sidebands.

Sidebands always come in pairs. The first pair of sidebands are known as first-order sidebands. One of the sidebands equals the sum of the frequencies of the modulator and the carrier, the other equals the difference. The amplitude of each sideband is half the product of the input amplitudes.

In ring modulation the first sound is a 200Hz sine wave and the second is a 500Hz sine wave. Ring modulation multiplies these two sounds together. The output is a new sound containing a pair of first-order sidebands. One sideband has a frequency of 700Hz, the sum of the two frequencies (500+200=700). The other sideband is 300Hz, the difference between the two frequencies (500-200=300).

Simple RM always uses two sine waves as input. The output is always a single sound containing a pair of frequencies called first-order sidebands. These first-order sidebands are all we hear, we do not hear the frequencies of the two original sine waves.

Whereas simple RM always uses two sine waves as inputs, complex RM requires one or both of the inputs to be a sound other than a sine wave.

The fourth sound in ring modulation is an example of complex RM. It is achieved by ring modulating speech with a 30Hz sine wave. What happens is that every frequency in the sample of speech is replaced by two sidebands. A frequency of 440Hz, for example, is replaced by two sidebands, 410Hz (440-30=410) and 470Hz (440+30=470), each sideband having half the amplitude of the frequency it replaced. The example mimics one of the most famous uses of complex RM, to create the sound of a Dalek in the BBC programme, Doctor Who.

RM is a simple and powerful synthesis technique. The output of simple RM is not harmonically rich: two frequencies in, two frequencies out. Its impact, however, is considerable because the carrier and modulator frequencies disappear altogether to be replaced by sidebands. In complex RM, the effect is even more pronounced, every frequency is replaced by a pair of sidebands, and the output has a distinctive hollow metallic sound.