Alpha-Stable Distributions in Signal Processing of Audio Signals

First, we propose two versions of a sliding window, block based parameter estimator for estimating the parameters in a symmetrical stable distribution. The proposed estimator is suitable for parameter estimation in audio signals. Second, the suitability of the stable distribution, for modelling audio signals, is discussed. For a broad class of audio signals, the distribution and the stationarity property are examinated. It is empirically shown that the class of stable distributions provides a better model for audio signals, than the Gaussian distribution model. Third, for demonstrating the applicability of stable distributions in audio processing, a classical problem from statistical signal processing, stochastic gradient adaptive filtering, is considered.