The acoustics of a room often refer to the quality of the room in terms of sound recording as well as sound reproduction. At low frequencies, where the wavelengths are of the same order of magnitude with the dimensions of the room, due to the standing waves phenomena, room modes are formed which can give rise to multiple irregularities and eventually damage the listening experience. In order to effectively address the problem at these frequencies, a thorough knowledge of the sound field in the room is often required. Through numerical studies, the sound field in the room could be simulated based on an FEM room model which would result in certain differences when comparing to the actual situation. On the other hand, the traditional experimental sampling of the sound field in a room often results in an impractical number of microphones.

This thesis focuses on the development of a sound field reconstruction framework that makes use of certain sparse representation and recovery algorithm to reconstruct the sound field of the room at low frequencies using a limited set of microphones. The reconstruction framework is then tested under different conditions and scenarios to prove its validity. Once the performance of the framework has been validated through both simulation and actual measurements, the reconstruction framework is investigated in detail regarding its application in the field of active modal equalization. These active absorption methods are of high interest in the field of modal equalization due to the fact that passive absorption method at low frequencies are more often than not ineffective. The reconstruction framework is then used to first assess the spatial performance of the active electroacoustic absorbers which consists of a current-driven system of loudspeakers in enclosures that aims to dampen room modes by achieving optimal target impedance in front of the loudspeaker membranes. In addition, a more complex applications of the reconstruction framework in which its reconstructed sound field can be used to fine tune the control parameters of the active absorbers is also investigated. The research shows promising results in both application of the reconstruction frameworks and open doors to further development in both the field of sound field reconstruction as well as room modes equalization.