Additive Synthesis

Discrete signals (bandlimited by half the sampling rate) may be represented as the sum of $N$ sinusoids of arbitrary amplitudes, phases, AND frequencies:

$$x(t)= \sum_{k=0}^{N}A_k\cos(\omega_kt+\phi_k)$$

We may therefore, synthesize a sound by setting up a bank of oscillators, each set to the appropriate amplitude, phase and frequency.

The output of each oscillator is added to produce a synthesized sound, and thus the synthesis technique is called additive synthesis.