Simulation of Textured Audio Harmonics Using Random Fractal Phaselets
We present a method of simulating audio signals using the principles of random fractal geometry which, in the context of this paper, is concerned with the analysis of statistically self-affine ‘phaselets’. The approach is used to generate audio signals that are characterised by texture and timbre through the Fractal Dimension such as those associated with bowed stringed instruments. The paper provides a short overview on potential simulation methods using Artificial Neural Networks and Evolutionary Computing and on the problems associated with using a deterministic approach based on solutions to the acoustic wave equation. This serves to quantify the origins of the ‘noise’ associated with multiple scattering events that characterise texture and timbre in an audio signal. We then explore a method to compute the phaselet of a phase signal which is the primary phase function from which a phase signal is, to a good approximation, a periodic replica and show that, by modelling the phaselet as a random fractal signal, it can be characterised by the Fractal Dimension. The Fractal Dimension is then used to synthesise a phaselet from which the phase function is computed through multiple concatenations of the phaselet. The paper provides details of the principal steps associated with the method considered and examines some example results, providing a URL to m-coded functions for interested readers to repeat the results obtained and develop the algorithms further.