Low Frequency Sound Field Reconstruction in Non-rectangular Room: A Numerical Validation

Characterization of sound fields in rooms has always been a challenging task. A faithful reconstruction of sound fields in rooms generally would require an impractically high number of microphones. At low frequencies, where sound field can be modeled as a finite superposition of modes, a combination of Matching Pursuit (MP) and Least-squares optimization can help interpolate the Room Impulse Responses using a relatively small number of measurements. Our research focuses on using this paradigm to obtain the low-frequency information of a room in a broader sense, where the spatial distribution of sound pressure in a non-rectangular reverberating room can be reconstructed and visually analyzed. Several evaluations are performed along the progression of the framework to confirm its validity. The modal parameters estimated by MP are also compared with those obtained by the Rational Fraction Polynomial method (global curve fitting). Finally, the reconstruction of sound field, which leads to the visualization of the spatial distribution of sound pressure at any chosen frequency in the range of study, is validated visually and numerically using a finite element method software for a non-rectangular room model. This demonstration provides an extensive look at the high robustness and reliability of the framework as a whole, which is crucial in terms of its practical implementations for room acoustics practitioners.