The Synthesis of Complex Audio Spectra by Means of Frequency Modulation

A new application of the well-known process of frequency modulation is shown to result in a surprising control of audio spectra. The technique provides a means of great simplicity to control the spectral components and their evolution in time. Such dynamic spectra are diverse in their subjective impressions and include sounds both known and unknown. In natural sounds the amplitudes of the frequency components of the spectrum are time-variant, or dynamic. The energy of the components often evolves in complicated ways, in particular, during the attack and decay portions of the sound. The temporal evolution of the spectrum is in some cases easily followed as with bells, whereas in other cases not, because the evolution occurs in a very short time period, but it is nevertheless perceived and is an important cue in the recognition of timbre. Many natural sounds seem to have characteristic spectral evolutions that, in addition to providing their "signature," are largely responsible for what we judge to be their lively quality. In contrast, it is largely the fixed proportion spectrum of most synthesized sounds that so readily imparts to the listener the electronic cue and lifeless quality. The special application of the equation for frequency modulation, described below, allows the production of complex spectra with very great simplicity. The fact that the temporal evolution of the frequency components of the spectrum can be easily controlled is perhaps the most striking attribute of the technique, for dynamic spectra are achieved only with considerable difficulty using current techniques of synthesis. At the end of this paper some simulations of brass, woodwind, and percussive sounds are given. The importance of these simulations is as much in their elegance and simplicity as it is in their accuracy. This frequency modulation technique, although not a physical model for natural sound, is shown to be a very powerful perceptual model for at least some.