Aalborg Universitet Non - Gaussian , Non - stationary and Nonlinear Signal Processing Methods - with Applications to Speech Processing and Channel Estimation

The Gaussian statistic model, despite its mathematical elegance, is found to be too factitious for many real world signals, as manifested by its unsatisfactory performance when applied to non-Gaussian signals. Traditional non-Gaussian signal processing techniques, on the other hand, are usually associated with high complexities and low data efficiencies. This thesis addresses the problem of optimum estimation of nonGaussian signals in computation-efficient and data-efficient ways. The approaches that we have taken exploit the high temporal-resolution non-stationarity or the underlying dynamics of the signals. The sub-topics being treated include: joint MMSE estimation of the signal DTFT magnitude and phase, high temporal-resolution Kalman filtering, blind de-convolution and blind system identification, and optimum non-linear estimation. Applications of the proposed algorithms to speech enhancement, non-Gaussian spectral analysis, noise-robust spectrum estimation, and blind channel equalization are demonstrated. The thesis consists of two parts, the Introduction and the Papers. The Introduction gives background information of the problems at hand, states the motivation of approaches taken, summarizes the state-of-the-art in literature, and describes our contributions briefly. The Papers presents our contributions in the form of published papers. The first part of the Papers (paper A and B) deals with the importance of phase in non-Gaussian signal estimation. Joint MMSE estimators of both magnitude spectra and phase spectra are developed. Application to the enhancement of noisy speech signals results in clearer sounds and higher SNR than frequency domain MMSE estimators. Here the non-Gaussianity of the speech signal is modeled by the linearity in the phase spectrum, and is enhanced by the joint estimator. This is in contrast to the spectral domain MMSE estimator (e.g., the Wiener filter), which is zero-phase. The second part of the Papers (paper C and D) attacks the non-Gaussian estimation problem with a purely temporal domain approach. It is recognized that a temporaldomain high-resolution non-stationary LMMSE estimator is able to extract structures in both magnitude and phase spectra at a lower complexity. For speech signals, the non-Gaussianity is represented by an excitation sequence with a rapidly varying vari-