Sound field reproduction is a fundamental problem in acoustic signal processing. The goal of sound field reproduction is to reproduce a desired sound field using an array of loudspeakers and the main task of sound field reproduction is to find out the weights applied to each loudspeaker. Most existing research concentrate on single zone sound field reproduction problem, such as Ambisonics and Wave Field Synthesis.
Multi-zone sound field reproduction is a technology that aims at providing listeners individual sound environment using only loudspeakers. The variety of approaches to multi-zone sound field reproduction can be roughly divided into two classes. One class is based on the fact that arbitrary sound fields may be expressed by means of spatial basis functions, such as cylindrical or spherical harmonics. The second class consists of multi-point approaches, where the sound field is optimized at sound pressure of control points in the least squares sense.
For both aforementioned multi-zone sound field reproduction methods, the number of samplings increases with the frequency of the desired sound field. For common reproduction scenes, it seems impractical to utilize too many microphones to capture the desired sound field.
To reduce the number of required microphones, researcher FENG Qipeng, YANG Feiran and YANG Jun from the Institute of Acoustics of the Chinese Academy of Sciences have recently proposed a multi-zone sound field reproduction method based on compressed sensing. The proposed method decomposes the desired sound field into a set of plane waves via -norm minimization (represents the sum of the absolute values of the vectors), which leads to a significantly reduced number of required microphones for accurate multi-zone sound field reproduction.
In many case of interest, the desired sound field, which originates from a small number of sound sources, is likely to be sparse in the source domain. Furthermore, due to the propagation characteristic of the spherical and cylindrical waves, the far field sound pressure distribution of a point or line sound source can be approximated as a plane wave.
Assuming that the desired multi-zone sound field contains a small number of far field sound sources, it is sparse in the plane wave domain, which means that the desired sound field can be decomposed into a few of weighted plane waves. According to concepts of compressed sensing, the desired sound field can be recovered from far fewer samples than required by the conventional methods of multi-zone sound field reproduction through optimization.
After the step of sparse plane wave decomposition, the complex multi-zone sound field reproduction problem is reduced to the plane wave reproduction over a single region. Existing single zone sound field reproduction approaches can be used in the reproduction step.
Any arbitrary desired sound field in a spatial region with no sources and no scatters can be represented by the Fourier-Bessel series expansion. Considering a uniformly distributed circular or spherical array of loudspeakers in anechoic chamber, the weights of loudspeakers can be expressed as a function of the desired sound field and positions of loudspeakers according to the continuous loudspeakers method.
Consequently, if the mode coefficients of the desired sound field can be calculated through the samplings, the accurate mutli-zone sound field reproduction can be achieved. Using the Jacobi-Anger expression, the plane wave can be further expressed as a set of cylindrical or spherical harmonics. If the desired multi-zone sound field can be decomposed into a series of weighted plane wave, the weights of loudspeakers can also be obtained.
To evaluate the performance of the multi-zone sound field reproduction system, the acoustic brightness contrast between two predefined zones and the normalized mean square error over the bright zone are defined. The more microphones are used, the better performance under the proposed method is.
In the case where only a few far field sound sources are present, the desired sound field can be described as a sparse set of plane waves based on compressed sensing methods. With a small number of microphones, the -norm minimization algorithms enable to obtain a good multi-zone sound field reproduction performance.
For the reproduction of under-sampled sound fields, simulations results demonstrate that the proposed method yields better performance than the two aforementioned approaches of multi-zone sound field reproduction, which means that the proposed method significantly reduces the number of required microphones.
FENG Qipeng, YANG Feiran, YANG Jun. Compressed Sensing based Multi-zone Sound Field Reproduction. The 13th IEEE International Conference on Signal Processing (November 6th to 9th, 2016, Chengdu, China).
Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China