Frequency Modulation (FM) Synthesis

The first commercial digital sound synthesis method was frequency modulation (FM) synthesis [31,34,32], invented by John Chowning, the founding director of CCRMA. FM synthesis was discovered and initially developed in the 1970s [31]. The technology was commercialized by Yamaha Corporation, resulting in the DX-7 synthesizer (1983), which was the first commercial digital synthesizer, and the OPL chipset, initially in the SoundBlaster PC sound card, and later a standard chipset required for ``SoundBlaster compatibility'' in computer multimedia support. The original pioneer patent expired in 1996, but additional patents were filed later. It is said that this technology lives on in cell-phone ring-tone synthesis.

As developed more fully in [232], the formula for elementary FM synthesis is given by

$$x(t) = A_c\sin[\omega_c t + \phi_c + A_m\sin(\omega_m t + \phi_m)]$$

where

$(A_c,\omega_c,\phi_c)$ specify the carrier sinusoid

$(A_m,\omega_m,\phi_m)$ specify the modulator sinusoid

Since instantaneous frequency is simply the time-derivative of instantaneous phase, FM can also be regarded as phase modulation