Synthesis of Environmental Sound Textures by Iterated Nonlinear Functions

In previous work, a class of digital sound synthesis methods was introduced using iterated nonlinear functions [1][2][3][4]. Within the phase space of any method in the class, we encounter regions of special interest where signals have peculiar self-similar structures (waveforms of multiple fractal contours) [5][6]. Due to the system dynamics, emergent properties in the output sound signal result into acoustic turbulences and other textural sound phenomena. Parallel work was pursued, both in computer music research [7] and in the auditory display of experimental data, using chaotic oscillators [8] (nonlinear pendulums are also illustrated in [9]). This paper discusses the use of iterated nonlinear functions in the modelling of the perceptual attributes in complex auditory images. Based on the chaotic dynamics in such algorithms, it is possible to create textural and environmental sound effects of a peculiar kind, hardly obtained with other methods. Examples include sound textures reminiscent of rains, thunderstorms and more articulated phenomena of acoustic turbulence. This research opens to new experiments in electroacoustic music and the creation of synthetic, but credible, auditory scenes in multimedia applications and virtual reality. 1. SURVEY OF FUNCTIONAL ITERATION SYNTHESIS Consider these definitions: A ⊂ R a set of “init values” for some iterated map process; G ⊂ Rm a set of parameters for the particular map considered; B ⊂ R a set of samples in the digital signal finally generated; and consider the cartesian product A × G ⊂ R × Rm. Let F be a map defined as