Alexander Mattioli Pasqual

Application of acoustic radiation modes in the directivity control by a spherical loudspeaker array

This work concerns the theoretical analysis and synthesis of sound fields by a compact spherical loudspeaker array. Such an electroacoustic device consists of several transducers mounted on a sphere-like structure, which are driven independently in order to achieve non-uniform directivity patterns. The control strategy usually adopted is to provide the array with some preprogrammed basic directivities corresponding to spherical harmonic functions. Thus, an arbitrary radiation pattern can be approximately achieved by changing the gains associated with these basic directivities. Here, a different approach based on the acoustic radiation modes of the array is proposed. Unlike spherical harmonics, radiation modes constitute a finite set of vectors that spans a subspace on which any radiation pattern the array is able to reproduce can be projected. Furthermore, radiation modes radiate sound energy independently. Since the eigenvalue analysis that must be carried out in order to obtain the modes leads also to their radiation efficiencies, the low frequency constraint in the directivity synthesis by a spherical array is naturally evaluated. Finally, it is useless to drive inefficient radiation modes. Therefore, the radiation mode approach leads to a reduced number of active channels, and to minimum source voltages for a given target directivity pattern.

Theoretical and experimental analysis of the electromechanical behavior of a compact spherical loudspeaker array for directivity control

Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.

Effects of enclosure design on the directivity synthesis by spherical loudspeaker arrays

Spherical loudspeaker arrays have been used to generate non‐uniform directivity patterns. It is known that the poor radiation efficiency of spherical sources and the loudspeaker electroacoustic behavior impose constraints on the directivity synthesis at low frequencies, which are aggravated as the source volume is made smaller. In this work, the effects of the enclosure design on the loudspeaker signal powers are analyzed. Two different approaches have been reported in literature, although quantitative comparisons have not been provided. In the first approach, the drivers share the same enclosure volume and in the second, they have their own independent sealed cavities. Here, an analytical model that takes into account the interior and exterior acoustic coupling is used in order to evaluate the voltages that must feed the array drivers. It is shown that the signal powers can be reduced at low frequencies by letting the drivers share the same enclosure volume. However, this leads to controllability problem...

Optimal array pattern synthesis with desired magnitude response

Letting Euclidean norm be the performance parameter, the task of finding the best approximation of a complex function in a finite dimension subspace leads to a convex optimization problem that can be easily solved by the least‐squares method. However, this procedure leads to a sub‐optimal solution in applications that have no phase requirements on the approximated function. In this case, semidefinite programming has been used to obtain optimal magnitude responses. In this work, this non‐convex optimization problem is dealt with by using an iterative method based on the least‐squares, which is illustrated on directivity synthesis by spherical loudspeaker arrays. Usually, instead of synthesize directly the desired pattern, the strategy adopted is to reproduce its truncated spherical harmonic representation. The truncation order is determined by the number of drivers of the spherical array. It is shown that truncation error and signal powers can be significantly reduced if phase error is neglected, providing...

Theoretical And Experimental Analysis Of The Electromechanical Behavior Of A Compact Spherical Loudspeaker Array For Directivity Control.

Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.