57,436 research outputs found
Frequency-Sliding Generalized Cross-Correlation: A Sub-band Time Delay Estimation Approach
The generalized cross correlation (GCC) is regarded as the most popular
approach for estimating the time difference of arrival (TDOA) between the
signals received at two sensors. Time delay estimates are obtained by
maximizing the GCC output, where the direct-path delay is usually observed as a
prominent peak. Moreover, GCCs play also an important role in steered response
power (SRP) localization algorithms, where the SRP functional can be written as
an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately,
the accuracy of TDOA estimates is affected by multiple factors, including
noise, reverberation and signal bandwidth. In this paper, a sub-band approach
for time delay estimation aimed at improving the performance of the
conventional GCC is presented. The proposed method is based on the extraction
of multiple GCCs corresponding to different frequency bands of the cross-power
spectrum phase in a sliding-window fashion. The major contributions of this
paper include: 1) a sub-band GCC representation of the cross-power spectrum
phase that, despite having a reduced temporal resolution, provides a more
suitable representation for estimating the true TDOA; 2) such matrix
representation is shown to be rank one in the ideal noiseless case, a property
that is exploited in more adverse scenarios to obtain a more robust and
accurate GCC; 3) we propose a set of low-rank approximation alternatives for
processing the sub-band GCC matrix, leading to better TDOA estimates and source
localization performance. An extensive set of experiments is presented to
demonstrate the validity of the proposed approach.Comment: Article accepted in IEEE/ACM Transactions on Audio, Speech, and
Language Processin
Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics
In the second part of this study and similarly with part one, the nonlinear
analysis of the solar flares index is embedded in the non-extensive statistical
theory of Tsallis [1]. The triplet of Tsallis, as well as the correlation
dimension and the Lyapunov exponent spectrum were estimated for the SVD
components of the solar flares timeseries. Also the multifractal scaling
exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of
the structure function exponents were estimated experimentally and
theoretically by using the entropy principle included in Tsallis non extensive
statistical theory, following Arimitsu and Arimitsu [2]. Our analysis showed
clearly the following: a) a phase transition process in the solar flare
dynamics from high dimensional non Gaussian SOC state to a low dimensional also
non Gaussian chaotic state, b) strong intermittent solar corona turbulence and
anomalous (multifractal) diffusion solar corona process, which is strengthened
as the solar corona dynamics makes phase transition to low dimensional chaos:
c) faithful agreement of Tsallis non equilibrium statistical theory with the
experimental estimations of i) non-Gaussian probability distribution function,
ii) multifractal scaling exponent spectrum and generalized Renyi dimension
spectrum, iii) exponent spectrum of the structure functions estimated for the
sunspot index and its underlying non equilibrium solar dynamics. e) The solar
flare dynamical profile is revealed similar to the dynamical profile of the
solar convection zone as far as the phase transition process from SOC to chaos
state. However the solar low corona (solar flare) dynamical characteristics can
be clearly discriminated from the dynamical characteristics of the solar
convection zone.Comment: 21 pages, 11 figures, 1 table. arXiv admin note: substantial text
overlap with arXiv:1201.649
Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics
In this study, the nonlinear analysis of the sunspot index is embedded in the
non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as
the correlation dimension and the Lyapunov exponent spectrum were estimated for
the SVD components of the sunspot index timeseries. Also the multifractal
scaling exponent spectrum, the generalized Renyi dimension spectrum and the
spectrum of the structure function exponents were estimated experimentally and
theoretically by using the entropy principle included in Tsallis non extensive
statistical theory, following Arimitsu and Arimitsu. Our analysis showed
clearly the following: a) a phase transition process in the solar dynamics from
high dimensional non Gaussian SOC state to a low dimensional non Gaussian
chaotic state, b) strong intermittent solar turbulence and anomalous
(multifractal) diffusion solar process, which is strengthened as the solar
dynamics makes phase transition to low dimensional chaos in accordance to
Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non
equilibrium statistical theory with the experimental estimations of i)
non-Gaussian probability distribution function, ii) multifractal scaling
exponent spectrum and generalized Renyi dimension spectrum, iii) exponent
spectrum of the structure functions estimated for the sunspot index and its
underlying non equilibrium solar dynamics.Comment: 40 pages, 11 figure
Practical implementation of nonlinear time series methods: The TISEAN package
Nonlinear time series analysis is becoming a more and more reliable tool for
the study of complicated dynamics from measurements. The concept of
low-dimensional chaos has proven to be fruitful in the understanding of many
complex phenomena despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
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