11,943 research outputs found
A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance
Room acoustic diffusers can be used to treat critical listening environments to improve sound quality. One popular class is Schroeder diffusers, which comprise wells of varying depth separated by thin fins. This paper concerns a new approach to enable the modelling of these complex surfaces in the time domain. Mostly, diffuser scattering is predicted using steady-state, single frequency methods. A popular approach is to use a frequency domain Boundary Element Method (BEM) model of a box containing the diffuser, where the mouth of each well is replaced by a compliant surface with appropriate surface impedance. The best way of representing compliant surfaces in time domain prediction models, such as the transient BEM is, however, currently unresolved. A representation based on surface impedance yields convolution kernels which involve future sound, so is not compatible with the current generation of time-marching transient BEM solvers. Consequently, this paper proposes the use of a surface reflection kernel for modelling well behaviour and this is tested in a time domain BEM implementation. The new algorithm is verified on two surfaces including a Schroeder diffuser model and accurate results are obtained. It is hoped that this representation may be extended to arbitrary compliant locally reacting materials
Time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, based on a combination of Gaussian receptive
fields over the spatial domain and first-order integrators or equivalently
truncated exponential filters coupled in cascade over the temporal domain.
Compared to previous spatio-temporal scale-space formulations in terms of
non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about (i) parameterizing the
intermediate temporal scale levels, (ii) analysing the resulting temporal
dynamics, (iii) transferring the theory to a discrete implementation, (iv)
computing scale-normalized spatio-temporal derivative expressions for
spatio-temporal feature detection and (v) computational modelling of receptive
fields in the lateral geniculate nucleus (LGN) and the primary visual cortex
(V1) in biological vision.
We show that by distributing the intermediate temporal scale levels according
to a logarithmic distribution, we obtain much faster temporal response
properties (shorter temporal delays) compared to a uniform distribution.
Specifically, these kernels converge very rapidly to a limit kernel possessing
true self-similar scale-invariant properties over temporal scales, thereby
allowing for true scale invariance over variations in the temporal scale,
although the underlying temporal scale-space representation is based on a
discretized temporal scale parameter.
We show how scale-normalized temporal derivatives can be defined for these
time-causal scale-space kernels and how the composed theory can be used for
computing basic types of scale-normalized spatio-temporal derivative
expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and
Vision, published online Dec 201
A Functional Wavelet-Kernel Approach for Continuous-time Prediction
We consider the prediction problem of a continuous-time stochastic process on
an entire time-interval in terms of its recent past. The approach we adopt is
based on functional kernel nonparametric regression estimation techniques where
observations are segments of the observed process considered as curves. These
curves are assumed to lie within a space of possibly inhomogeneous functions,
and the discretized times series dataset consists of a relatively small,
compared to the number of segments, number of measurements made at regular
times. We thus consider only the case where an asymptotically non-increasing
number of measurements is available for each portion of the times series. We
estimate conditional expectations using appropriate wavelet decompositions of
the segmented sample paths. A notion of similarity, based on wavelet
decompositions, is used in order to calibrate the prediction. Asymptotic
properties when the number of segments grows to infinity are investigated under
mild conditions, and a nonparametric resampling procedure is used to generate,
in a flexible way, valid asymptotic pointwise confidence intervals for the
predicted trajectories. We illustrate the usefulness of the proposed functional
wavelet-kernel methodology in finite sample situations by means of three
real-life datasets that were collected from different arenas
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