César D. Salvador

A Compact Representation of the Head-Related Transfer Function Inspired by the Wavelet Transform on the Sphere

The head-related transfer function (HRTF) characterizes the propagation of sound from its source to the listeners ears. It is commonly used in the research of spatial sound and its applications. The HRTF takes different values depending on the sources position relative to the listener and its frequency. Storing its values directly results in considerably large data sets. Previous research to encode the HRTF using harmonic functions cannot handle local features efficiently. This paper advances a new analysis method to represent raw HRTF data using local functions of the azimuth and elevation angles. The proposal treats features of different scales separately, in a manner similar to the wavelet transform. This allows us to compress HRTF data considerably while accurately preserving its features at all scales. The proposal yields better accuracy than harmonic analysis methods for the finer spatial patterns, this holds even when our method us.es more aggressive compression.

Boundary Matching Filters for Spherical Microphone and Loudspeaker Arrays

Conversion of microphone array signals into loudspeaker array signals is an essential process in high-definition spatial audio. This paper presents the theory of boundary matching filters (BMFs) for spherical array signal conversion. BMFs adapt the physical boundary conditions used during recording to the ones required for reproduction by relying on a theoretical framework provided by the Kirchhoff–Helmholtz integral equation (KHIE). Computationally, array signal conversion is performed in a transform domain where sound fields are represented in terms of spherical harmonic functions. Related research on transform-domain signal conversion filters is interpreted in the context of the KHIE. The case of a rigid recording boundary and an open reproduction boundary is addressed. The proposed rigid-to-open BMFs provide a suitable basis for designing gain-limited filters to deal with the problem of excessive gains at certain frequency bands, observed when using high-resolution arrays. Spatial, spectral, and temporal effects in sound field reconstruction when finite numbers of transducers are used in anechoic conditions are investigated analytically and exemplified numerically. Results show that the proposed gain-limited rigid-to-open BMFs outperform the existing gain-limited filters based on Tikhonov regularization because they reduce the spatial discretization effects and yield impulse responses that are more localized around their main peaks.

A local representation of the head-related transfer function

Spatial descriptions of the head-related transfer function (HRTF) using spherical harmonics, which is commonly used for the purpose, consider all directions simultaneously. However, in perceptual studies, it is necessary to model HRTFs with different angular resolutions at different directions. To this end, an alternative spatial representation of the HRTF, based on local analysis functions, is introduced. The proposal is shown to have the potential to describe the local features of the HRTF. This is verified by comparing the reconstruction error achieved by the proposal to that of the spherical harmonic decomposition when reconstructing the HRTF inside a spherical cap.

Sound field interpolation in the spatial domain with a rigid spherical microphone array

Sound field interpolation aims to calculate sound fields at arbitrary points from original measurements at discrete points. Rigid spherical microphone arrays are effective for interpolation because they can capture sound from several directions with uniform resolution. Interpolation from spherical array measurements is typically based on the spherical Fourier transform and assumes no prior knowledge concerning the source positions. The spherical Fourier transform, however, yields results whose accuracy strongly depends on microphone positioning and the inversion method used for its computation. When knowledge of the source positions is available, the pressure generated at any point on the rigid spherical baffle can be estimated with an existing physical model. This model was used in this study to define an analytic transfer function that relates the pressure at two arbitrary points on a rigid sphere. Based on this analytic function, an interpolation method in the spatial domain is presented as an alternat...

Prediction Method for Compression of Spherical Microphone Array Signals Using Geometric Information

Previously, we proposed a method to achieve high-precision measurement systems to record 3D sound-space information. This enables the transmission of spatial sound to distant places, and enables its preservation. Our method, named Symmetrical object with ENchased ZIllion microphones (SENZI), was implemented using a spherical microphone array with 252 microphones. It was applied to the recording of 3D sound-space information. The microphone positions follow an icosahedral pattern. Reproducing a 3D sound space recorded with the SENZI implementation requires transmission of all the microphone signals. However, the necessarily large number of channels produce vast amounts of data. Therefore, it is important to compress these data without markedly reducing the accuracy of the reproduced 3D sound-space. In this paper, we propose a multi-channel sound signal compression technique for recordings done with a SENZI microphone array. Inter-channel correlation in the SENZI system is extremely high because the microphones are arranged densely on the sphere. Our proposed method exploits this correlation to predict some microphone signals from those recorded by microphones that are aligned with the vertices of the underlying icosahedron. The possibility of recovering some microphone signals from those of their neighbors is verified through computer simulations of a SENZI array.