Multiply — Gain & Modulation
Multiplication is one of the simplest operations in DSP — and one of the most useful. If an audio sample is a number, multiplying that number changes its size. Do it to every sample and we change the signal level.
1. Multiply a signal by a constant
These Max-style number boxes show one instantaneous sample from the moving waveform. Watch the numbers: input × multiplier = output.
Same signal.
Half the amplitude.
Silence.
Same amplitude, opposite polarity.
2. Now replace the constant with a changing number
This is the important jump. The multiplier does not have to stay at 0.5 or 1. It can change from sample to sample — automatically.
Tremolo: an LFO continuously changes the multiplier. The waveform itself remains the source; its amplitude rises and falls because we are multiplying it by a moving control value.
3. Hear multiplication
Start the tone, then move Rate, Depth, change modulation mode, or adjust Audio volume. The audio engine reads those controls continuously, so you hear the multiplication change in real time.
4. You've already used this everywhere
audio × constant
audio × envelope
audio × slow LFO
audio × ramp
grain × window shape
audio × calculated changing gain
5. Control-rate versus audio-rate multiplication
If the multiplier changes slowly, we hear the level changing: fades, envelopes and tremolo. If it changes at audio rate, multiplication can create new spectral components — the basis of amplitude modulation and closely related techniques.
We do not need the full maths yet. The important point is that the operation has not changed: it is still multiplication.
6. One operation, many processors
x[n] means the current input sample. g[n] is the gain/control value at that moment. y[n] is the resulting output sample.