Near-field Acoustic Holography Based On Compressed Sensing And Its DSP Implementation

Most of the early sound source identification methods cannot meet the sound source localization requirements.With the continuous advancement of electronic technology,digital signal processing technology and computer technology,new techniques for noise source identification such as beamforming,wavelet analysis,sound intensity measurement and near-field acoustic holography are gradually established.The NAH technique collects the sound pressure or particle velocity information on the holographic measuring surface near the sound source.The sound pressure or normal velocity of the particle on the reconstructed surface is calculated from the sound pressure data of the holographic surface by using the spatial transform mathematical model of the acoustic components of reconstructed surface and holographic surface.A mathematical model for solving the normalized particle velocity and particle pressure based on the planar near-field acoustic holography is formulated.The distance between the holographic plane and the sound source plane,and the measured data volume on the holographic plane are identified as two key factors affecting the reconstruction accuracy.Through theoretical analysis and numerical simulation experiments,it is found that the conventional planar near-field acoustic holography cannot overcome the ill-posed problem of reconstruction by using regularization and filtering.In order to reduce the amount of data sampling and data processing,and to further improve the imaging accuracy,the research were carried out from three aspects that are the signal sparse representation,measurement matrix and signal reconstruction algorithms.The relationship between the commonly used measurement matrix and signal sparsity was investigated.Theoretical analysis and simulation verification were carried out under different reconstruction algorithms for different sparsity and observation values.The results of this study will be helpful to compress the measured data and improve the quality of sound field reconstruction.Acompressedsensingplanarnear-fieldacousticholography（SL0-CS-PNAH）method based on a smoothing l₀ norm is proposed.According to the isolated and discontinuous characteristics of measured sound pressure on the holographic surface,the symlets8 wavelet function is used to construct the sparse basis of the normalized velocity of the reconstructed plane particles.In order to obtain a measurement matrix conforming to the Restricted Isometric Property（RIP）condition in the SL0-CS-PNAH method and to compressively sample sparse signals or sparsely-expressed signals,it is necessary that the Rayleigh first integral formula should be discretized with the distribution of sound field information on the holographic surface and the reconstructed surface.The minimum l₀ norm mathematical model of the sparse vector is deduced.The optimization problem under this model is solved by using the smooth l₀ norm algorithm under the constraints of the complex acoustic pressure,the target sparse vector and the sensing matrix of holographic particles.The optimal sparse solution is obtained,and multiplied by the sparse basis to obtain the surface normal velocity of reconstruction.Under the same sampling rate and compression ratio,the numerical simulation which includes OMP-CS-PNAH,SL0-CS-PNAH,CPNAH and SP-CS-PNAH was carried out.After analyzing the simulation results,it is concluded that the reconstruction accuracy of SL0-CS-PNAH is higher.A sound data acquisition and processing platform was built by using ADMP401 MEMS microphone linear array and TI TMS320C6747 digital signal processor.The sound pressure data on the holographic surface is acquired by parallel movement of the MEMS microphone linear array according to the set scanning spacing,and the digital signal is obtained by the analog-digital conversion circuit.The complex sound pressure data matrix is obtained by using fast Fourier transform.The complex sound pressure matrix is preprocessed by using transfer function method to obtain the finally corrected sound pressure data.The compressed sensing planar near-field acoustic holography method based on the smoothing l₀ norm developed in MATLAB software was ported to the TI Code Composer Studio development environment.Then,the final sound pressure data is transmitted to the TMS320C6747 digital signal processor for experimental verification.The platform can be used for basic experimental research of algorithm validation,sound signal,and development of acoustic algorithms.