Fractal additive synthesis

Abstract

In this article, we outlined time-frequency techniques that, when brought together, form the basis for FAS. The method is based on an exact orthogonal transform, the HBWT. The FAS model can be seen as an intelligent spectrogram, i.e., as a spectrogram where the frequency bins (the HBWT subbands) are adapted to the spectrum of the analyzed sound by tuning the number of channels P to the period of the sound. Local cosines replace the classical windowed complex exponentials, whose main property is that the basis elements form sidebands of the harmonics rather than being centered on the harmonics themselves. The wavelet transform nonuniform frequency subdivision characteristic is exploited to synthesize each sideband of the harmonic peaks by means of colored noise, generating an approximate pseudoperiodic 1/f behavior. The pseudoharmonics are modeled by narrow sidebands whose weights can be generated by means of amplitude envelopes and phase functions in a complexified HBWT domain. We also showed how perceptual criteria can be employed to reduce the number of synthesis parameters. The possibility of independently controlling the noisy components and the harmonic terms and the definition of parameters such as volumes and envelopes for all of the components independently provide powerful tools for processing voiced-sound for sound design purposes