Yan Wang

A spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in Fourier domain. It allows successful reconstructions surrounding the array, but the accuracy will be degraded at a distance. In order to extend the effective reconstruction to the entire cavity, a plane-wave basis in space domain is used owing to its non-decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity. The sensitivity to measurement noise, the effects of the numbers of plane waves, and measurement positions are discussed. Simulations show that under the same measurement conditions, the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency, that is, the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measurement position into a global one. An experiment was conducted inside an aircraft cabin mock-up for validation. Additionally, this method provides an alternative possibility to recover the coefficients of high order spherical wave functions in a global coordinate system without coordinate translations with respect to local origins.

A low frequency sound field within a cylindrical cavity can be well approximated by a sparse set of Fourier−Bessel series in a spherical coordinate system. The approximation accuracy can be guaranteed as long as the series coefficients are well estimated by use of spherical microphone arrays (SMA). Conventional methods like spherical Fourier transform and Helmholtz equation least square require a large number of sensors, and it is difficult to estimate the high order coefficients in the presence of sensor noise. To cope with these issues, compressive sensing (CS) is utilized and compared with the conventional methods. In this study, the estimate of the high order coefficients from contaminated measurements is examined, and the effect of modal behavior is analyzed. Numerical simulations show that sensors can be significantly saved especially for high order cavity modes due to the low sparsity of coefficients which is also stable as the modal frequency increases, and the overall accuracy is also improved. The optimal SMA configuration for the use of CS is studied. A large SMA with omni-microphone deployed by the Fliege sampling scheme is suggested. The CS results are finally validated through the good simulated reconstructions of cylindrical cavity modes.

In a spherical coordinate system, interior sound field can be expressed in terms of a series of Fourier-Bessel expansions. The process that obtains the expansion coefficients by use of a microphone array (e.g., a spherical microphone array) is called spatial encoding. Until now spatial encoding has mainly been examined in a free field or a diffuse field which can be modeled as a sum of plane waves. For spatial encoding within an enclosure at low frequencies, special challenges would be encountered in two aspects. First, the expansions are influenced by array configurations. Second, an acoustic mode based model instead of a plane wave based one should be considered. This study focuses on these challenges. Different kinds of array configurations were compared specifically at low frequencies, and the spatial encoding for the cylindrical cavity modes was investigated. It was found that the spherical array with cardioid microphones was optimal when kr<1, the cavity modes can be effectively represented by only a sparse subset of expansion coefficients and a good reproduction can be achieved even outside the spherical valid region, which demonstrates an effective alternative way to describe the cylindrical cavity modes and can be implemented efficiently in practice.