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Sound field recording using spherical harmonics (SH) has been widely used. However, too many microphones are needed when recording sound fields over large areas, due to the capture of the higher order of spherical harmonic coefficients. The theory of GO in deep learning inspired us. With training the data much less than all GO’s legal positions data, the Alpha Go has defeated top GO players. According to the information learned from a specific dataset, the higher spherical harmonics coefficients may be estimated with few captured sound pressures. In this paper, a learning-based approach for estimation of the SH coefficients has been investigated. In the proposed approach, SH coefficients are estimated with a feed-forward neural network (FNN) based on measurements of a spherical array. We generate a uniformly distributed dataset, try to evaluate the method on an average situation. Moreover, with the real sound field data in the SOFiA dataset, we try to evaluate the performance of our method when the correlations of data are weak. Experimental results show that the proposed approach achieves higher estimation accuracy of SH coefficients than a previously reported method. In simulations, 9 microphones’ performance using the proposed approach can approximate an array with 16 microphones. The experiments confirmed the feasibility of estimating the SH coefficients with the data-driven method. Thus in a specific application, it can be used to reduce the required number of microphones.

Sound field reproduction using Higher-order Ambisonics (HOA) has many studies in recent years. However, in the HOA, sound fields are reproduced with the least square solution of spherical harmonics (SH) coefficients and not the global sound fields. In this paper, we try to reduce the reproduction error with a data-driven method. As we all known, the Generative Adversarial Networks (GAN) can be used to generate data similar to a data set. With the GAN, the target sound fields are converted to sound fields that can be reproduced accurately in the proposed approach. The data set of target sound fields is updated with the generated fields which have less reproduction error, and thus reproduction errors are reduced. We simulated the performance with four loudspeakers, sound fields of 4 orders SH coefficients are reproduced with GAN and HOA at 1000 Hz, with average reproduction errors of 0.3 and 0.6, respectively. Simulations show that the space between the least-square solution and the optimization solution is reduced with our method. Furthermore, the performances of HOA are optimized.