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.

Acoustical behavior of a room for a given position of microphone and sound source is usually described using the room impulse response. If we rely on the standard uniform sampling, the estimation of room impulse response for arbitrary positions in the room requires a large number of measurements. In order to lower the required sampling rate, some solutions have emerged that exploit the sparse representation of the room wavefield in the terms of plane waves in the lowfrequency domain. The plane wave representation has a simple form in rectangular rooms. In our solution, we observe the basic axial modes of the wave vector grid for extraction of the room geometry and then we propagate the knowledge to higher order modes out of the low-pass version of the measurements. Estimation of the approximate structure of the kspace should lead to the reduction in the terms of number of required measurements and in the increase of the speed of the reconstruction without great losses of quality.

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In order to address optimal acoustic control in rooms, an accurate characterization of the room shape and wall properties is required. There are only a few approaches that model the wall impedances. Most of them rely on finite difference time domain methods, which are limited to shoebox-shaped rooms and only valid at low frequencies (non-rectangular rooms and high frequencies lead to extremely high computational complexity). In order to overcome these limits, we propose the estimation of walls’ acoustic impedances based on the analysis of the room impulse responses. In room impulse responses, the early reflections’ amplitudes are proportional to the reflection coefficient of the corresponding wall element. The location of points on the walls (origins) for the first and second order echoes can be easily determined for a known room. The values of impedances at the origins of the first order echoes are determined directly from the room impulse response. The second order echoes' represent a product of the influence of wall points that belong to its path. Values of individual impedances are extracted from these echoes by overlapping origins of first order echoes of one receiver’s position with one origin of the second order echoes of another receiver’s position.