Modeling resonances with phase modulated self-similar processes [speech processing example]

In this paper, we propose a nonlinear model for time-varying random resonances where the instantaneous phase (and frequency) of a sinusoidal oscillation is allowed to vary proportionally to a random process that belongs to the class of α-stable self-similar stochastic processes. This is a general model that includes phase modulations by fractional Brownian motion or fractional stable Levy motion as special cases. We explore theoretically this random modulation model and derive analytically its autocorrelation and power spectrum. We also propose an algorithm to fit this model to arbitrary resonances with random phase modulation. Further, we apply the above ideas to some speech data and demonstrate that the model is suitable for fricative sounds.