Estimation of spherical harmonic coefficients in sound field recording using feed-forward neural networks
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Estimation of spherical harmonic coefficients in sound field recording using feed-forward neural networks Lingkun Zhang1,2 · Xiaochen Wang1,2
· Ruimin Hu1,2 · Dengshi Li1,3 · Weipin Tu1,3
Received: 12 October 2019 / Revised: 18 July 2020 / Accepted: 24 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Spherical harmonics · Microphone array · Sound field recording · Sound field reproduction
Xiaochen Wang
[email protected] 1
National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University, Wuhan 430072, China
2
Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, Wuhan 430072, China
3
Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China
Multimedia Tools and Applications
1 Introduction The spherical harmonics theory is first applied in sound field reproduction in [12, 13]. Then spherical harmonic analysis has been used in more and more array signal processing [3, 29, 30]. Sound field recording is one of the most important applications [2]. Spherical harmonic is a set of basis functions and can represent any general sound field. A microphone array captures discrete sound pressures, and then spherical harmonic coefficients can be calculated to reconstruct the continuous sound field [9, 22, 23]. Many factors affect the accuracy of the calculated coefficients. In recent years, many research studies have mainly focused on the geometry of the microphone array [5, 38, 39]. Spherica
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