Smooth Transition Region Design For Broadband Beamforming Problem

In this thesis,we first review the research history of microphone array signal process-ing.Then,we briefly describes the common design of beamforming problem.The broadband beamformer design of microphone array can be formulated into an optimization problem.For the actual response function of the optimal solution,as the filter length becomes large,there exists serious vibration in the transition region.For this,we formulate a modified beamformer design problem such that the actual response function is very smooth in transition region,while the performance remains very close to that of original problem.Furthermore,the per-formance analysis is given for the original beamformer design and smooth transition region design.Numerical examples is also shown to verify the effectiveness of the proposed design.The content of this thesis is organized as follows.The first chapter is the introduction of the principle of signal processing.We summarize the characteristics and application fields of microphone array signal processing.In chapter 2,we introduce some common optimization problems such as semi-infinite programming and positive semidefinite programming,which are widely used in microphone array design.In chapter 3,we introduce the design of microphone array beamforming.For the different objective functions,the beamformer design problems of microphone array are also different.Therefore,we introduce five kinds of objective functions and their corresponding beamformer design problems.In chapter 4,we first introduce the robust problem of microphone array beamformer de-sign in the first subsection.Then,we introduce the Gibbs phenomenon which offten appears in filter design problem.In the second and third subsections,we consider the robust problems of microphone array design in the case of far field and near field,respectively.As the filter length is relatively large,there is a serious phenomenon of Gibbs in the transition region,al-though the optimality of the solution is guaranteed.Therefore,we design the beamforming problem with smooth transition region.For this,by adding a suitable smooth desired response in the transition region,we formulate and solve a new design problem.Next,the performance of the problem have also been analyzed.Finally,numerical examples are given to illustrate that adding the smooth desired response in the transition region can eliminate the Gibbs phe-nomenon perfectly.In chapter 5,we summarize the conclusion in this thesis and make a prospect for future research.