Low frequency sound field reconstruction in a non-rectangular room using a small number of microphones

Abstract

An accurate knowledge of the sound field distribution inside a room is required to identify and optimally locate corrective measures for room acoustics. However, the spatial recovery of the sound field would result in an impractically high number of microphones in the room. Fortunately, at low frequencies, the possibility to rely on a sparse description of sound fields can help reduce the total number of measurement points without affecting the accuracy of the reconstruction. In this paper, the use of Greedy algorithm and Global curve-fitting techniques are proposed, in order to first recover the modal parameters of the room, and then to reconstruct the entire enclosed sound field at low frequencies, using a reasonably low set of measurements. First, numerical investigations are conducted on a non-rectangular room configuration, with different acoustic properties, in order to analyze various aspects of the reconstruction frameworks such as accuracy and robustness. The model is then validated with an experimental study in an actual reverberation chamber. The study yields promising results in which the enclosed sound field can be faithfully reconstructed using a practically feasible number of microphones, even in complex-shaped and damped rooms.

Spatial reconstruction of sound fields using local and data-driven functions

“…Sparse solutions, with few non-zero elements in x, can be robust in underdetermined cases 43 and have recently proven to be particularly useful in sound field reconstruction. [17][18][19]22,23,41,42 Sparse solutions are either found by greedy methods that progressively add one non-zero coefficient at a time, 32,33 or approximated by convex relaxation to the ' 1 -norm, 43 as in the least absolute shrinkage and selection operator (LASSO). 44 From the coefficient estimate x, the sound pressure can be reconstructed as…”

“…As such, the selection of a suitable set of functions to represent the sound field is critical, and ultimately, a defining element for achieving successful reconstructions. 8,[16][17][18][19] General solutions to the wave equation (such as plane, cylindrical or spherical waves) are often employed as basis functions in sound field reconstruction. Such analytical models are well suited provided that their geometrical properties conform with expected wave phenomena.…”

“…In the case of the sound field in a room, it is observed that a limited number of spherical waves would typically suffice to represent the early part of a room impulse response, 18,22 and the low frequency response of a rectangular room is, in general, well approximated by a limited number of propagating plane waves, as a result of the low modal overlap. 17,19,20,23,24 Yet, the sound field in a room is often highly complex. In particular, the sound field in a room at mid and high frequencies is characterized by a high overlap of normal modes, which confer a seemingly chaotic structure to the observed field.…”

Spatial reconstruction of the sound field in a room in the modal frequency range using Bayesian inference

“…16,17 Recently, a data driven deep-learning based approach for sound field reconstruction in rectangular rooms was proposed by Llu ız et al 20 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. 21 Beyond that, numerical reconstruction approaches exist based on the inverse boundary element method (IBEM) [22][23][24] or the inverse finite element method (IFEM). 25 These approaches solve the inverse reconstruction problem to provide a point estimate, i.e., one value of the sound pressure or other field quantities at the given reconstruction points.…”