Additive Synthesis

Discrete signals may be represented as the sum of sinusoids of arbitrary amplitudes, phases, and frequencies.

Sounds may be synthesized by setting up a bank of oscillators, each set to the appropriate amplitude, phase and frequency:

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

Since the output of each oscillator is added to produce the synthesized sound, the technique is called additive synthesis.

Additive synthesis provides maximum flexibility in the types of sound that can be synthesized and can realize tones that are ``indistinguishable'' from the original.

Signal analysis, which provides amplitude, phase and frequency functions for a signal, is often a prerequisite to additive synthesis, which is sometimes also called Fourier recomposition.