Space-Time-Frequency Processing of Acoustic Wave Fields: Theory, Algorithms, and Applications

Abstract

Abstract-Consider a nonparametric representation of acoustic wave fields that consists of observing the sound pressure along a straight line or a smooth contour defined in space. The observed data contains implicit information of the surrounding acoustic scene, both in terms of spatial arrangement of the sources and their respective temporal evolution. We show that such data can be effectively analyzed and processed in what we call the space-time-frequency representation space, consisting of a Gabor representation across the spatio-temporal manifold defined by the spatial axis and the temporal axis . In the presence of a source, the spectral patterns generated at have a characteristic triangular shape that changes according to certain parameters, such as the source distance and direction, the number of sources, the concavity of , and the analysis window size. Yet, in general, the wave fronts can be expressed as a function of elementary directional components-most notably, plane waves and far-field components. Furthermore, we address the problem of processing the wave field in discrete space and time, i.e., sampled along and , where a Gabor representation implies that the wave fronts are processed in a block-wise fashion. The key challenge is how to chose and customize a spatio-temporal filter bank such that it exploits the physical properties of the wave field while satisfying strict requirements such as perfect reconstruction, critical sampling, and computational efficiency. We discuss the architecture of such filter banks, and demonstrate their applicability in the context of real applications, such as spatial filtering, deconvolution, and wave field coding.

Applications of short space-time fourier analysis in digital acoustics

“…This implies that p(r, t) behaves harmonically across both space and time, and is therefore efficiently represented by P (Φ, Ω) [3]. One particular transform pair is known as the plane wave, characterized by the input p(r, t) = e jΩ 0 (t+u·r/c) .…”

“…The inverse formula can be interpreted as the continuous sum of all the "signal blocks" indexed by (r0, t0), and it requires that wr(r) and wt(t) have unit area [3]. The definition in (3) is characterized by a partitioning of the (r0, t0, Φ, Ω)-hyperspace into uniform hypercubic regions spanning the dimensions of space and time and the respective frequencies.…”

Spatial perception reproduction of sound event based on sound properties

“…Based on position vectors of loudspeakers synthesis, VBAP enables the use of an arbitrary number of loudspeakers arranged in a circle or sphere and is readily available for users in common environments for real time processing. However, VBAP is valid only at frequencies roughly below 500 Hz [11,12] and it is complicated if the loudspeaker setup is not spherical.…”

Three-dimensional audio parametric encoding based on perceptual characteristics of spatial cue1

“…Pinto, et al [7] converted collected sound field data into frequency domain using time-space fold transformation and achieved WFS signal expression using 2D temporal frequency. Additionally, models for rapid attenuating omnidirectional wave and slowly attenuating directional wave were established, and compression was achieved by discarding the omnidirectional wave.…”