1,092 research outputs found
Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case
The article reviews the statistical theory of signal detection in application
to analysis of deterministic gravitational-wave signals in the noise of a
detector. Statistical foundations for the theory of signal detection and
parameter estimation are presented. Several tools needed for both theoretical
evaluation of the optimal data analysis methods and for their practical
implementation are introduced. They include optimal signal-to-noise ratio,
Fisher matrix, false alarm and detection probabilities, \F-statistic,
template placement, and fitting factor. These tools apply to the case of
signals buried in a stationary and Gaussian noise. Algorithms to efficiently
implement the optimal data analysis techniques are discussed. Formulas are
given for a general gravitational-wave signal that includes as special cases
most of the deterministic signals of interest.Comment: Revised version of 2006-07-26; published version available at
http://www.livingreviews.org/lrr-2005-
A constructive and unifying framework for zero-bit watermarking
In the watermark detection scenario, also known as zero-bit watermarking, a
watermark, carrying no hidden message, is inserted in content. The watermark
detector checks for the presence of this particular weak signal in content. The
article looks at this problem from a classical detection theory point of view,
but with side information enabled at the embedding side. This means that the
watermark signal is a function of the host content. Our study is twofold. The
first step is to design the best embedding function for a given detection
function, and the best detection function for a given embedding function. This
yields two conditions, which are mixed into one `fundamental' partial
differential equation. It appears that many famous watermarking schemes are
indeed solution to this `fundamental' equation. This study thus gives birth to
a constructive framework unifying solutions, so far perceived as very
different.Comment: submitted to IEEE Trans. on Information Forensics and Securit
Detecting Baryon Acoustic Oscillations
Baryon Acoustic Oscillations are a feature imprinted in the galaxy
distribution by acoustic waves traveling in the plasma of the early universe.
Their detection at the expected scale in large-scale structures strongly
supports current cosmological models with a nearly linear evolution from
redshift approximately 1000, and the existence of dark energy. Besides, BAOs
provide a standard ruler for studying cosmic expansion. In this paper we focus
on methods for BAO detection using the correlation function measurement. For
each method, we want to understand the tested hypothesis (the hypothesis H0 to
be rejected) and the underlying assumptions. We first present wavelet methods
which are mildly model-dependent and mostly sensitive to the BAO feature. Then
we turn to fully model-dependent methods. We present the most often used method
based on the chi^2 statistic, but we find it has limitations. In general the
assumptions of the chi^2 method are not verified, and it only gives a rough
estimate of the significance. The estimate can become very wrong when
considering more realistic hypotheses, where the covariance matrix of the
measurement depends on cosmological parameters. Instead we propose to use a new
method based on two modifications: we modify the procedure for computing the
significance and make it rigorous, and we modify the statistic to obtain better
results in the case of varying covariance matrix. We verify with simulations
that correct significances are different from the ones obtained using the
classical chi^2 procedure. We also test a simple example of varying covariance
matrix. In this case we find that our modified statistic outperforms the
classical chi^2 statistic when both significances are correctly computed.
Finally we find that taking into account variations of the covariance matrix
can change both BAO detection levels and cosmological parameter constraints
A time-frequency based method for the detection and tracking of multiple non-linearly modulated components with births and deaths
International audienceThe estimation of the components which contain the characteristics of a signal attracts great attention in many real world applications. In this paper, we address the problem of the tracking of multiple signal components over discrete time series. We propose an algorithm to first detect the components from a given time-frequency distribution and then to track them automatically. In the first place, the peaks corresponding to the signal components are detected using the statistical properties of the spectral estimator. Then, an original classifier is proposed to automatically track the detected peaks in order to build components over time. This classifier is based on a total divergence matrix computed from a peak-component divergence matrix that takes account of both amplitude and frequency information. The peak-component pairs are matched automatically from this divergence matrix. We propose a stochastic discrimination rule to decide upon the acceptance of the peak-component pairs. In this way, the algorithm can estimate the number, the amplitude and frequency modulation functions, and the births and the deaths of the components without any limitation on the number of components. The performance of the proposed method, a post-processing of a time-frequency distribution is validated on simulated signals under different parameter sets. The method is also applied to 4 real-world signals as a proof of its applicability. Index Terms—Time-frequency domain, multicomponent, peak detection, component tracking, amplitude and frequency modulation , nonlinear, nonstationary, births and death
- …