A comparison of measured room acoustics metrics using a spherical microphone array and conventional methods

The traditional microphone configuration used to measure room impulse responses (IRs) according to ISO 3382:2009 is an omnidirectional and figure-8 microphone pair. IRs measurements were taken in a 2500-seat auditorium to determine how the results from a spherical microphone array (an mh acoustics Eigenmike-em32) compare to those from the traditional microphone setup (a Brüel & Kjær Type-4192 omnidirectional microphone and a Sennheiser MKH30 figure-8 microphone). Measurements were obtained at six receiver locations, with three repetitions each in order to first evaluate repeatability. The metrics considered in this study were: reverberation time (T30), early decay time (EDT), clarity index (C80), strength (G), lateral energy fraction (J_LF) and late lateral energy level (L_J). Before calculating these quantities, the IRs were filtered to equalize the frequency response of the microphones and sound source. For the spherical array measurements, the omnidirectional (monopole) and figure-8 (dipole) patterns were extracted using beamforming. In terms of repeatability, the average standard deviation of the three measurements at each receiver location averaged across all metrics, receivers, and octave bands was found to be 0.01 just noticeable differences (JNDs). The analysis comparing the measurements from the two microphone configurations yielded differences which were less than 1 JND for the majority of metrics, with a few exceptions of EDT and C80 slightly above 1 JND. Based on this case study, these results indicate that spherical microphone arrays can be used to obtain valid room IR measurements, which will allow for the development of new metrics utilizing the higher spatial resolution made possible with spherical arrays.     

A class of deformational flow test cases for linear transport problems on the sphere

A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed.     

Spherical harmonics MUSIC versus conventional MUSIC

With the three-dimensional symmetry and wide potential application, spherical array signal processing has been a hot research area for years. This paper devotes to the direction-of-arrival (DOA) estimation of the spherical arrays. Based on the orthogonality of the sensors’ location, MUSIC algorithm in spherical space is proposed, named as SH-MUSIC. Similar to beamspace MUSIC, spherical harmonics transformation is operated before MUSIC algorithm and a better performance is gotten because SH-MUSIC utilizes the array configuration’s orthogonality. On account of the transformation matrix’s orthogonality, spherical harmonics transformation is suggested to be operated firstly in other improved MUSIC algorithms without rejection, and it is demonstrated in beamspace MUSIC. In addition, owing to the tiny error between the steering vectors and the spherical harmonics with high order, sphere array data models including open sphere and rigid sphere are constructed. Simulation proves SH-MUSIC to be effective. Moreover, experimental data from a rigid sphere microphone array is dealt with by SH-MUSIC and the DOAs are estimated accurately.     

Numerical simulation of core convection by a multi-layer semi-implicit spherical spectral method

A semi-implicit multi-layer spherical spectral method for simulating stellar core convection is described. The fully compressible three-dimensional hydrodynamic equations with rotation and energy generation are solved. Prognostic variables are expressed as finite sums of spherical harmonics in the horizontal directions and handled by the finite difference method in the radial direction. The stratified approximation is used to simplify the nonlinearity to quadratic. A multi-layer scheme is employed to overcome the time step problem arising from shrinking grid sizes in the physical space near the center of the star. Despite of the different spectral truncations in different layers, round-off conservation of the total mass and total angular momentum of the whole domain can be maintained, and were confirmed numerically. The code is parallelized; with 12 processors the speedup factor is about 9. The solutions of model core convection with and without rotation are discussed.     

Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.     

Tchebycheff-Fourier级数的Vallce Poussin平均逼近函数类Lip α

本文考虑用ＴｃｈｅｂｙｃｈｅｆＦｏｕｒｉｅｒ级数的ＶａｌéｅＰｏｕｓｉｎ平均逼近函数类Ｌｉｐα,在ｆ（ｘ）∈Ｃ［－１,１］时获得了逼近阶及逼近误差的表达式,推广并较大地改进了文献［１,２］中的有关结果．     

A Radial Derivative with Boundary Values of the Spherical Poisson Integral

A formula of a radial derivative is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates .     

Sundual characterizations of the translation group of

We characterize the first three sundual spaces of , with respect to the translation group of .

     

Randomised circular means of Fourier transforms of measures

We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.

     

A Point Balance Algorithm for the Spherical Code Problem

The Spherical Code (SC) problem has many important applications in such fields as physics, molecular biology, signal transmission, chemistry, engineering and mathematics. This paper presents a bilevel optimization formulation of the SC problem. Based on this formulation, the concept of balanced spherical code is introduced and a new approach, the Point Balance Algorithm (PBA), is presented to search for a 1-balanced spherical code. Since an optimal solution of the SC problem (an extremal spherical code) must be a 1-balanced spherical code, PBA can be applied easily to search for an extremal spherical code. In addition, given a certain criterion, PBA can generate efficiently an approximate optimal spherical code on a sphere in the n-dimensional space ⁿ. Some implementation issues of PBA are discussed and putative global optimal solutions of the Fekete problem in 3, 4 and 5-dimensional space are also reported. Finally, an open question about the geometry of Fekete points on the unit sphere in the 3-dimensional space is posed.