Abstract
Spatial characterization of the sound field in a room is a challenging task, as it usually requires a large number of measurement points. This paper presents a probabilistic approach for sound field reconstruction in the modal frequency range for small and medium-sized rooms based on Bayesian inference. A plane wave expansion model is used to decompose the sound field in the examined domain. The posterior distribution for the amplitude of each plane wave is inferred based on a uniform prior distribution with limits based on the maximum sound pressure observed in the measurements. Two different application cases are studied, namely a numerically computed sound field in a non-rectangular two-dimensional (2D) domain and a measured sound field in a horizontal evaluation area of a lightly damped room. The proposed reconstruction method provides an accurate reconstruction for both examined cases. Further, the results of Bayesian inference are compared to the reconstruction with a deterministic compressive sensing framework. The most significant advantage of the Bayesian method over deterministic reconstruction approaches is that it provides a probability distribution of the sound pressure at every reconstruction point, and thus, allows quantifying the uncertainty of the recovered sound field.
Highlights
Capturing the spatial properties of a sound field in a room is important in various applications, e.g., in sound field analysis,1 source localization,2,3 and room compensation and equalization for sound field control systems.4,5 Typically, an extensive number of measurements is required in order to determine the frequency response experimentally with basic sampling techniques within an extended region of a room.6 In order to minimize the experimental effort, recent research has focused on reducing the number of measurement points.direct measurements are performed
This paper presents a probabilistic approach for sound field reconstruction in the modal frequency range for small and medium-sized rooms based on Bayesian inference
A Bayesian inference (BI) approach to reconstruct the sound field in an enclosure has been presented
Summary
Capturing the spatial properties of a sound field in a room is important in various applications, e.g., in sound field analysis, source localization, and room compensation and equalization for sound field control systems. Typically, an extensive number of measurements is required in order to determine the frequency response experimentally with basic sampling techniques within an extended region of a room. In order to minimize the experimental effort, recent research has focused on reducing the number of measurement points. The unknown amplitudes of the wave propagation model need to be determined based on measured sound pressure data at a limited number of observation points. This results in an inverse acoustic problem, which is usually ill posed. Pham Vu and Lissek introduced a method based on a greedy algorithm and a global curve-fitting technique to recover the modal parameters of a non-rectangular room and to reconstruct the entire sound field at low frequencies..
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