3,077 research outputs found
An optimally concentrated Gabor transform for localized time-frequency components
Gabor analysis is one of the most common instances of time-frequency signal
analysis. Choosing a suitable window for the Gabor transform of a signal is
often a challenge for practical applications, in particular in audio signal
processing. Many time-frequency (TF) patterns of different shapes may be
present in a signal and they can not all be sparsely represented in the same
spectrogram. We propose several algorithms, which provide optimal windows for a
user-selected TF pattern with respect to different concentration criteria. We
base our optimization algorithm on -norms as measure of TF spreading. For
a given number of sampling points in the TF plane we also propose optimal
lattices to be used with the obtained windows. We illustrate the potentiality
of the method on selected numerical examples
Superposition frames for adaptive time-frequency analysis and fast reconstruction
In this article we introduce a broad family of adaptive, linear
time-frequency representations termed superposition frames, and show that they
admit desirable fast overlap-add reconstruction properties akin to standard
short-time Fourier techniques. This approach stands in contrast to many
adaptive time-frequency representations in the extant literature, which, while
more flexible than standard fixed-resolution approaches, typically fail to
provide efficient reconstruction and often lack the regular structure necessary
for precise frame-theoretic analysis. Our main technical contributions come
through the development of properties which ensure that this construction
provides for a numerically stable, invertible signal representation. Our
primary algorithmic contributions come via the introduction and discussion of
specific signal adaptation criteria in deterministic and stochastic settings,
based respectively on time-frequency concentration and nonstationarity
detection. We conclude with a short speech enhancement example that serves to
highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio
Adaptive absorbing boundary conditions for Schrodinger-type equations: application to nonlinear and multi-dimensional problems
We propose an adaptive approach in picking the wave-number parameter of
absorbing boundary conditions for Schr\"{o}dinger-type equations. Based on the
Gabor transform which captures local frequency information in the vicinity of
artificial boundaries, the parameter is determined by an energy-weighted method
and yields a quasi-optimal absorbing boundary conditions. It is shown that this
approach can minimize reflected waves even when the wave function is composed
of waves with different group velocities. We also extend the split local
absorbing boundary (SLAB) method [Z. Xu and H. Han, {\it Phys. Rev. E},
74(2006), pp. 037704] to problems in multidimensional nonlinear cases by
coupling the adaptive approach. Numerical examples of nonlinear Schr\"{o}dinger
equations in one- and two dimensions are presented to demonstrate the
properties of the discussed absorbing boundary conditions.Comment: 18 pages; 12 figures. A short movie for the 2D NLS equation with
absorbing boundary conditions can be downloaded at
http://home.ustc.edu.cn/~xuzl/movie.avi. To appear in Journal of
Computational Physic
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