Research On Uniform Sound Field Reconstruction Algorithm Based On Least Square Method

The sound field control technology refers to spatial sound field reproduction or control of the spatial sound field distribution mode by controlling the amplitude and phase of the input signals of each loudspeaker.With the development of sound field control technology,it can effectively solve the listener’s desire to produce different acoustic environments in different areas without interfering with each other.Therefore,sound field control technology is needed to segment the spatial sound field and reconstruct the target sound field in a specific area,while reducing the impact on other areas.The sound quality in the control area also needs to meet certain requirements,so this thesis studies the higher uniformity in the reconstructed sound field area.The sound field control technology is mainly sound field reconstruction technology and sound field energy control technology.The sound pressure matching technology based on the least square method can obtain a good reconstruction sound quality,and can generate a sound field with a specific shape according to the distribution of the target area.This thesis makes an in-depth study on the algorithm.In order to study the ill-posed problem in the solution of sound field control technology based on least square method,this thesis uses two directions to optimize the problem.One is to adopt Tikhonov regularization.This thesis first discusses the effect of regularization parameters on the uniform sound field,and introduces generalized cross-validation and L-curve method for parameter selection.Experiments and simulations prove that the L-curve method balances the reconstruction error and speaker power,and has a wider practical significance.The second is the direct optimization method using the complex method,which avoids the ill-posed problem caused by the traditional generalized inversion during the solution process,and uses the speaker phase iteration to solve the weight.The innovations and main contents of this article are as follows:(1)In order to solve the problem that the least squares sound field reconstruction algorithm has low-band fluctuations and low sound energy in a wide frequency band,Tikhonov regularization is proposed for optimization.The simulation results prove that Tikhonov regularization can effectively improve the ill-posed problem and flexibly adjust the uniformity of the sound field.(2)Aiming at the problem of regularization parameter selection,L-curve method and GCV method are introduced for parameter selection.Simulation and experiment prove that both methods can improve the low-band fluctuations,but the L-curve method can better achieve the balance between reconstruction error and speaker power,which has practical significance.At the same time,the effect of speaker array parameters on sound field reconstruction is studied,which provides guidance for the selection of speaker array parameters in practical applications.(4)A direct optimization method is proposed.The algorithm solves the speaker weight coefficients in an iterative manner,which can avoid the ill-posed problem in the traditional solution process and improve the uniformity of the traditional least square reconstruction algorithm.The research results in this thesis prove that the uniform sound field reconstruction technology based on the least square method can achieve uniform distribution of the sound field,and effectively and flexibly realize the adjustment of the sound field,which has important guiding significance for the realization of the uniform sound field reconstruction technology.