Frequency Modulation (FM) Synthesis

The first commercial digital sound synthesis method was Frequency Modulation (FM) synthesis [38,41,39], invented by John Chowning, the founding director of CCRMA. FM synthesis was discovered and initially developed in the 1970s [38]. The technology was commercialized by Yamaha Corporation, resulting in the DX-7 (1983), the first commercial digital music 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 discussed more fully in [264, p. 44], the formula for elementary FM synthesis is given by

$$x(t) = A_c\sin[\omega_c t + \phi_c + A_m\sin(\omega_m t + \phi_m)] \protect$$ (G.2)

where

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

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

An example computer-music-style diagram is shown in Fig.G.6. Since the instantaneous frequency of a sinusoid is simply the time-derivative of its instantaneous phase, FM can also be regarded as phase modulation (PM). It is highly remarkable that such a simple algorithm can generate such a rich variety of musically useful sounds. This is probably best understood by thinking of FM as a spectral modeling technique, as will be illustrated further below.

Figure G.6: Simple FM brass synthesis.