Design Of Microphone Array Beamformer By Window Function Method

Microphone array play important role in acoustic signal processing.The beamformer design of microphone array can be transformed into a semi-infinite programming problem where the coefficients of all FIR(finite impulse response)filters are the decision variables and the actual frequency response function fits to a given desired frequency response function.Discretization method is required to solve this problem.However,as the number of discrete points grows and the filter length increases,this problem will become more complicated,and finding the optimal solution becomes more difficult.In this thesis,a fast window function method is proposed to solve this problem in real time.The main contents of this paper are organized as follows:The first chapter is the introduction,where the basic principles of digital signal processing and FIR filter are first introduced.Next,we introduce the principle of the microphone array optimal in the case of near field model and far-field model,respectively.Finally,we descript the criteria of beamformer design,such as the mean square error,maximum error and signal to noise ratio.The second chapter is the introduction of microphone array beamformer design problem.We consider the microphone array beamformer design problems in the cases of near field and far field,respectively.The first is the establishment of the microphone array beamformer design problem.Next,by solving the limit value of the optimal value as the filter length tends to infinity,we formulate a series of specific optimization problems and obtain the infimum of the optimal values,which is the performance limit.Finally,we verify the conclusion from two numerical examples.The third chapter is the real time design of microphone array beamformer problem.We proposes a method to design the filter in real time by using the window function.First,we obtain the optimal frequency response function.Then,the coefficients of the optimal frequen-cy response vector can be directly calculated.Next,we formulate a minimax optimization problem by using the window function,and obtain the FIR filter coefficients.Due to the Gibbs phenomenon,there exists oscillation in the discontinuous point of frequency.We modify the design such that the coefficients can be corrected.Finally,the efficiency and effectiveness of the method are verified by numerical examples.The fourth chapter is to summarize the research of this paper and make a prospect for the subsequent research work.