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Uncertainty principles and ideal atomic decomposition
 IEEE Transactions on Information Theory
, 2001
"... Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every d ..."
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Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discretetime signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time/frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the `1 norm of the coe cients among all decompositions. Here \highly sparse " means that Nt + Nw < p N=2 where Nt is the number of time atoms, Nw is the number of frequency atoms, and N is the length of the discretetime signal.
Vocal Command Signal Segmentation and Phonemes Classification.
, 1999
"... this paper we study a set of vocal command signals recorded in a noisy environment. We describe and use Fang's segmentation algorithm ..."
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this paper we study a set of vocal command signals recorded in a noisy environment. We describe and use Fang's segmentation algorithm
Multivariate Bayes Wavelet Shrinkage and Applications
"... ABSTRACT In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive wit ..."
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ABSTRACT In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented. KEY WORDS: methods Bayes shrinkage, wavelets, discrete wavelet transformation, data denoising, MCMC
Bayes Wavelet Shrinkage and Applications
"... this paper, a different and more elastic hierarchical prior is elicited on the model parameters describing the wavelet coefficients. Exact Bayesian analysis is impossible and the shrinkage is performed through a Markov chain Monte Carlo scheme. An application on a noisy signal is presented. ..."
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this paper, a different and more elastic hierarchical prior is elicited on the model parameters describing the wavelet coefficients. Exact Bayesian analysis is impossible and the shrinkage is performed through a Markov chain Monte Carlo scheme. An application on a noisy signal is presented.
Variable Amplitude Loading Strains Data Distribution using Probability Density Function and Power Spectral Density
"... density Abstract. This paper presents a relative study on variable amplitude (VA) strain data distribution using the approach of probability density function (PDF) and power spectral density (PSD). PDF is a technique to identify the probability of the value falling within a particular interval, and ..."
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density Abstract. This paper presents a relative study on variable amplitude (VA) strain data distribution using the approach of probability density function (PDF) and power spectral density (PSD). PDF is a technique to identify the probability of the value falling within a particular interval, and a PSD is to measure the power of a signal by converting it from the time domain to the frequency domain. The objective of this study is to observe the applicability of both techniques in detecting the pattern behaviour in terms of energy and probability distribution. For this reason, a set of case study data consist of nonstationary VA pattern with a random behaviour was used. This kind of data was measured by fixing a strain gauge that connected to the strain data acquisition on the lower suspension arm of a midsized sedan car. The data was measured for 60 seconds at the sampling rate of 500 Hz, which gave 30,000 discrete points. The distribution of collected data was then calculated and analysed in the form of both PDF and PSD, and they were then compared for further analysis. The findings from this study are expected for determining the pattern behaviour that exists in VA strain signals.