Synthesis Tutorial 3: Using Amplitude Modulation
Ring modulation and amplitude modulation
Amplitude modulation (AM) involves changing the amplitude of a carrier signal using the output of another modulator signal. In the specific AM case of ring modulation (discussed in the previous tutorial) the two signals are simply multiplied. In the more general case, the modulator is used to alter the carrier's amplitude, but is not the sole determinant of it. To put it another way, the modulator can cause fluctuation of amplitude around some value other than 0. The example below illustrates the difference between ring modulation and more common amplitude modulation.
The example on the left is 1/4 second of a 100 Hz cosine multiplied by a 4 Hz cosine; the amplitude of both cosines is 1. In the example on the right, the 4 Hz cosine has an amplitude of 0.25, which is used to vary the amplitude of the 100 Hz tone ±0.25 around 0.75 (going as low as 0.5 and as high as 1.0). The two main differences are a) the AM example never goes all the way to 0, whereas the ring modulation example does, and b) the ring modulation is perceived as two amplitude dips per modulation period (thus creating a tremolo effect at twice the rate of the modulation) whereas the AM is perceived as a single cosine fluctuation per modulation period.
The two MSP patches that made these examples are shown below.
The difference in effect is due to the constant value ofin the AM patch, which is varied by a modulator of lesser amplitude. This constant value can be thought of as the carrier's amplitude, which is varied by the instantaneous amplitude of the modulator. The amplitude still varies according to the shape of the modulator, but the modulator is not centered on 0.
Implementing AM in MSP
The tutorial patch is designed in such a way that the DC offset of the modulator is always 1 minus the amplitude of its sinusoidal variation. That way, the peak amplitude of the modulator is always 1, so the product of carrier and modulator is always 1. A separate *~ object is used to control the over-all amplitude of the sound.
Achieving different AM effects
The primary merit of AM lies in the fact that the intensity of its effect can be varied by changing the amplitude of the modulator.
Amplitude modulation produces sidebands - additional frequencies not present in the carrier or the modulator - equal to the sum and the difference of the frequencies present in the carrier and modulator. The presence of a DC offset (technically energy at 0 Hz) in the modulator means that the carrier tone remains present in the output, too (which is not the case with ring modulation).
When there is a harmonic relationship between the carrier and the modulator, the frequencies produced belong to the harmonic series of a common fundamental, and tend to fuse more as a single complex tone. For example, with a carrier frequency of 1000 Hz and a modulator at 250 Hz, you will hear the frequencies 250 Hz, 750 Hz, 1000 Hz, and 1250 Hz; the 1st, 3rd, 4th, and 5th harmonics of the fundamental at 250 Hz.
It is worth noting that any audio signals can be used as the carrier and modulator tones, and in fact many interesting results can be obtained by amplitude modulation with complex tones. In a later tutorial, we'll look at how to perform amplitude modulation on the sound coming into our computer.
The amplitude of an audio (carrier) signal can be modulated by another (modulator) signal, either by simple multiplication (ring modulation) or by adding a time-varying modulating signal to a constant signal (DC offset) before multiplying it with the carrier signal (amplitude modulation). The intensity of the amplitude modulation can be controlled by increasing or reducing the amplitude of the time-varying modulator relative to its DC offset. When the modulator has a DC offset, the carrier frequency will remain present in the output sound, along with sidebands at frequencies determined by the sum and the difference of the carrier and the modulator. At sub-audio modulating frequencies, amplitude modulation is heard as tremolo; at audio frequencies the carrier, modulator, and sidebands are all heard as a chord or as a complex tone.