Reconstruction Of Sound Pressure Field Function Based On Compressive Sampling

The classical Shannon sampling theory can only handle bandlimited signals.Therefore, in the field of signal processing, the problem of sampling nonbandlimitedsignals has received much attention. Compressive sampling has shown that for signalswith a parametric representation, precise results can be achieved with low samplingrate. Compared with related traditional algorithms, the algorithms proposed in thepaper lead to more precise results and very low sampling rate for hardware circuit,when approaching the problem of acoustic field reconstruction. The conclusion inthe paper can be applied to sound source location, virtual source generation, gettingHead-related Transfer Function, etc.A mathematical model with weak noise is provided for recovering narrowbandsound signal. The characteristic of the signal in frequency domain is analyzed, inorder to propose two methods to reproduce Dirac impulses with complex amplitudes:the whole-signal method and the double-channel method. Based on these methods, aspectral compressive sampling scheme is proposed for the narrowband signal, whichis then applied to sound source location.Sampling models for linear and circular microphone array are provided for theplenacoustic function (PAF) in free field. In the case of weak noise, reconstructionmethod for the PAF along time axis using compressive sampling is proposed, with s-inc function, Gauss function and E-spline as sampling kernel respectively. The featureof the PAF in both time and frequency domain is analyzed, which leads to the recon-struction methods: recovering the PAF along space axis using Shannon theory, andreproducing the spatio-temporal by parametric-depended method. Under hypothesisof innegligible noise, reconstruction method for white noise, narrowband noise andbandlimited noise is proposed respectively. A generalized expression in time domain is provided for the plenacoustic function(PAF) in closed space. According to the expression along time axis, the performanceof classical compressive sampling typically degrades if the impulses contain closelyspaced components or in the presence of many Dirac impulses. In this paper, theunstable results of classical compressive sampling is analyzed, based on which themethod leading to more precise results is proposed. This method is then improved forless searching cost. In closed space, the expression of PAF along time axis in timedomain is analyzed, based on which a proper reconstruction method is proposed.All the theoretical schemes proposed in the paper are confirmed by simulationand experimental results. The spectral compressive sampling scheme proposed forthe narrowband signal requires a much lower sampling rate and theoretically moreprecise time-delay estimation. The proposed PAF reconstruction methods based oncompressive sampling can be achieved with very low sampling rate, and result in moreprecise results. Meanwhile, for impulses containing closely spaced components, thealgorithm proposed requires less searching and computing cost.