23,090 research outputs found
Extracting a shape function for a signal with intra-wave frequency modulation
In this paper, we consider signals with intra-wave frequency modulation. To
handle this kind of signals effectively, we generalize our data-driven
time-frequency analysis by using a shape function to describe the intra-wave
frequency modulation. The idea of using a shape function in time-frequency
analysis was first proposed by Wu. A shape function could be any periodic
function. Based on this model, we propose to solve an optimization problem to
extract the shape function. By exploring the fact that s is a periodic
function, we can identify certain low rank structure of the signal. This
structure enables us to extract the shape function from the signal. To test the
robustness of our method, we apply our method on several synthetic and real
signals. The results are very encouraging
Data-Driven Time-Frequency Analysis
In this paper, we introduce a new adaptive data analysis method to study
trend and instantaneous frequency of nonlinear and non-stationary data. This
method is inspired by the Empirical Mode Decomposition method (EMD) and the
recently developed compressed (compressive) sensing theory. The main idea is to
look for the sparsest representation of multiscale data within the largest
possible dictionary consisting of intrinsic mode functions of the form , where , consists of the
functions smoother than and . This problem can
be formulated as a nonlinear optimization problem. In order to solve this
optimization problem, we propose a nonlinear matching pursuit method by
generalizing the classical matching pursuit for the optimization problem.
One important advantage of this nonlinear matching pursuit method is it can be
implemented very efficiently and is very stable to noise. Further, we provide a
convergence analysis of our nonlinear matching pursuit method under certain
scale separation assumptions. Extensive numerical examples will be given to
demonstrate the robustness of our method and comparison will be made with the
EMD/EEMD method. We also apply our method to study data without scale
separation, data with intra-wave frequency modulation, and data with incomplete
or under-sampled data
Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations
The Immersed Boundary method has evolved into one of the most useful
computational methods in studying fluid structure interaction. On the other
hand, the Immersed Boundary method is also known to suffer from a severe
timestep stability restriction when using an explicit time discretization. In
this paper, we propose several efficient semi-implicit schemes to remove this
stiffness from the Immersed Boundary method for the two-dimensional Stokes
flow. First, we obtain a novel unconditionally stable semi-implicit
discretization for the immersed boundary problem. Using this unconditionally
stable discretization as a building block, we derive several efficient
semi-implicit schemes for the immersed boundary problem by applying the Small
Scale Decomposition to this unconditionally stable discretization. Our
stability analysis and extensive numerical experiments show that our
semi-implicit schemes offer much better stability property than the explicit
scheme. Unlike other implicit or semi-implicit schemes proposed in the
literature, our semi-implicit schemes can be solved explicitly in the spectral
space. Thus the computational cost of our semi-implicit schemes is comparable
to that of an explicit scheme, but with a much better stability property.Comment: 40 pages with 8 figure
Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model
By performing estimates on the integral of the absolute value of vorticity along a local vortex line segment, we establish a relatively sharp dynamic growth estimate of maximum vorticity under some assumptions on the local geometric regularity of the vorticity vector. Our analysis applies to both the 3D incompressible Euler equations and the surface quasi-geostrophic model (SQG). As an application of our vorticity growth estimate, we apply our result to the 3D Euler equation with the two anti-parallel vortex tubes initial data considered by Hou-Li [12]. Under some additional assumption on the vorticity field, which seems to be consistent with the computational results of [12], we show that the maximum vorticity can not grow faster than double exponential in time. Our analysis extends the earlier results by Cordoba-Fefferman [6, 7] and Deng-Hou-Yu [8, 9]
Sparse Time-Frequency decomposition for multiple signals with same frequencies
In this paper, we consider multiple signals sharing same instantaneous
frequencies. This kind of data is very common in scientific and engineering
problems. To take advantage of this special structure, we modify our
data-driven time-frequency analysis by updating the instantaneous frequencies
simultaneously. Moreover, based on the simultaneously sparsity approximation
and fast Fourier transform, some efficient algorithms is developed. Since the
information of multiple signals is used, this method is very robust to the
perturbation of noise. And it is applicable to the general nonperiodic signals
even with missing samples or outliers. Several synthetic and real signals are
used to test this method. The performances of this method are very promising
Coexistence of strong nematic and superconducting correlations in a two-dimensional Hubbard model
Using a dynamic cluster quantum Monte Carlo approximation, we study a
two-dimensional Hubbard model with a small orthorhombic distortion in the
nearest neighbor hopping integrals. We find a large nematic response in the
low-frequency single-particle scattering rate which develops with decreasing
temperature and doping as the pseudogap region is entered. At the same time,
the d-wave superconducting gap function develops an s-wave component and its
amplitude becomes anisotropic. The strength of the pairing correlations,
however, is found to be unaffected by the strong anisotropy, indicating that
d-wave superconductivity can coexist with strong nematicity in the system.Comment: 4 pages, 4 figures, published as PRB 84, 220506(R) (2011
Speaker Re-identification with Speaker Dependent Speech Enhancement
While the use of deep neural networks has significantly boosted speaker
recognition performance, it is still challenging to separate speakers in poor
acoustic environments. Here speech enhancement methods have traditionally
allowed improved performance. The recent works have shown that adapting speech
enhancement can lead to further gains. This paper introduces a novel approach
that cascades speech enhancement and speaker recognition. In the first step, a
speaker embedding vector is generated , which is used in the second step to
enhance the speech quality and re-identify the speakers. Models are trained in
an integrated framework with joint optimisation. The proposed approach is
evaluated using the Voxceleb1 dataset, which aims to assess speaker recognition
in real world situations. In addition three types of noise at different
signal-noise-ratios were added for this work. The obtained results show that
the proposed approach using speaker dependent speech enhancement can yield
better speaker recognition and speech enhancement performances than two
baselines in various noise conditions.Comment: Acceptted for presentation at Interspeech202
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