On optimization methods for speech signal processing

Abstract

This thesis is concerned with optimization used in speech signal processing, including filters design problem, equalizer, and beamformer design problems. All these three problems play an essential role in signal speech processing. Firstly, the minimax design of infinite impulse response(IIR) filter is considered. Partial fraction method is applied to decompose the transfer function into a sum of low order fractions; as a result, the minimax IIR filter design problem can be formulated with the stability condition as constraints. Then, among different possible decompositions of the transfer function, it can be proved that the second order decomposition can always achieve a good approximation to the optimal solution. Based on the second order decomposition formulation, several numerical experiments have been conducted, and better IIR filters can be designed using the proposed method compared with existing methods in the literature. Secondly, a fixed equalizer aiming at noise reduction is designed by optimizing objective measures. There are many objective quality measures in speech quality testing, and one of the most popular ones is PESQ, and another latest measure is STOI. In this part, both of these two measures are considered as optimization criteria when designing weights of equalizers. To enhance robustly, there is a pre-training part of this method, and the average weights of the training section achieve as the coefficients of the fixed equalizer. Thirdly, array gain optimization methods are considered in speech enhancement. Algorithms, LS, and SNR, are used to find optimal weights, and the improved performance using these two methods are presented. From the results, we could see that LS concentrate more on distortion control comparing with SNIR method, but SINR performs better in noise suppression than LS. Besides, in the experimental part, the results consist of two parts, including the real data recorded by sensors and the created signals calculated by a transfer function.