The Experts below are selected from a list of 16599 Experts worldwide ranked by ideXlab platform
Alexandru Isar - One of the best experts on this subject based on the ideXlab platform.
-
review on the statistical decorrelation of the wavelet packet coefficients of a band limited wide sense Stationary Random Process
Signal Processing, 2007Co-Authors: Abdourrahmane M. Atto, Dominique Pastor, Alexandru IsarAbstract:This paper is a contribution to the analysis of the statistical correlation of the wavelet packet coefficients resulting from the decomposition of a Random Process, Stationary in the wide-sense, whose power spectral density (PSD) is bounded with support in [-@p,@p]. Consider two quadrature mirror filters (QMF) that depend on a parameter r, such that these filters tend almost everywhere to the Shannon QMF when r increases. The parameter r is called the order of the QMF under consideration. The order of the Daubechies filters (resp. the Battle-Lemarie filters) is the number of vanishing moments of the wavelet function (resp. the spline order of the scaling function). Given any decomposition path in the wavelet packet tree, the wavelet packet coefficients are proved to decorrelate for every packet associated with a large enough resolution level, provided that the QMF order is large enough and above a value that depends on this wavelet packet. Another consequence of our derivation is that, when the coefficients associated with a given wavelet packet are approximately decorrelated, the value of the autocorrelation function of these coefficients at lag 0 is close to the value taken by the PSD of the decomposed Process at a specific point. This specific point depends on the path followed in the wavelet packet tree to attain the wavelet packet under consideration. Some simulations highlight the good quality of the ''whitening'' effect that can be obtained in practical cases.
-
On the asymptotic decorrelation of the wavelet packet coefficients of a wide-sense Stationary Random Process
2006Co-Authors: Abdourrahmane M. Atto, Dominique Pastor, Alexandru IsarAbstract:This paper is a contribution to the analysis of the statistic al correla- tion of the wavelet packet coefficients resulting from the dec omposition of a Random Process, Stationary in the wide-sense, whose pow er spectral density is bounded with support in [ − π, π ]. Consider two quadrature mirror filters (QMF) that depend on a pa- rameter r , such that these filters tend almost everywhere to the Shan- non QMF when r increases. The parameter r is called the order of the QMF under consideration. The order of the Daubechies filters (resp. the Battle-Lemari ́e filters) is the number of vanishing moments of the wavelet function (resp. the spline order of the scaling function). Given any decomposition path in the wavelet packet tree, the wavelet packet coefficients are proved to decorrelate for every packe t associated with a large enough resolution level, provided that the QMF o rder is large enough and above a value that depends on this wavelet packet. Another consequence of our derivation is that, when the coeffi cients associated with a given wavelet packet are approximately de correlated, the value of the autocorrelation function of these coefficients a t lag 0 is close to the value taken by the power spectral density of the decompos ed Process at a specific point. This specific point depends on the path fol lowed in the wavelet packet tree to attain the wavelet packet under co nsideration. Some simulations highlight the good quality of the "whiteni ng" effect that can be obtained in practical cases.
Moe Z. Win - One of the best experts on this subject based on the ideXlab platform.
-
a unified spectral analysis of generalized time hopping spread spectrum signals in the presence of timing jitter
IEEE Journal on Selected Areas in Communications, 2002Co-Authors: Moe Z. WinAbstract:This paper characterizes the power spectral density (PSD) of various time-hopping spread-spectrum (TH-SS) signaling schemes in the presence of Random timing jitter, which is characterized typically by a discrete-time Stationary Random Process (independent of the TH sequences and data sequence) with known statistical properties. A flexible model for a general TH-SS signal is proposed and a unified spectral analysis of this generalized TH-SS signal is carried out using a systematic and tractable technique. The key idea is to express the basic baseband pulse in terms of its Fourier transform which allows flexibility in specifying different TH formats throughout the general derivation. The power spectrum of various TH-SS signaling schemes can then be obtained as a special case of the generalized PSD results. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific results are then given for the cases of practical interest, namely, uniform and Gaussian distributed jitter. Applications of this unified spectral analysis includes: (1) clocked TH by a Random sequence; (2) framed TH by a Random sequence; and (3) framed TH by a pseudoRandom periodic sequence. Detailed descriptions of these different TH techniques are given where the first two techniques employ a Random sequence (stochastic model) and the third technique employs a pseudoRandom sequence (deterministic model).
-
on the power spectral density of digital pulse streams generated by m ary cycloStationary sequences in the presence of Stationary timing jitter
IEEE Transactions on Communications, 1998Co-Authors: Moe Z. WinAbstract:The spectral occupancy and composition of a chosen digital signaling technique when the data pulse stream is nonideal, due, for instance, to implementation imperfections, are important considerations in the design of a practical communication system. One source of imperfection is timing jitter where the rising and falling transitions do not occur at the nominal data transition time instants; nevertheless, the time instants are offset by Random amounts relative to the nominal one. The amount of timing shift per transmission interval is Random and is typically characterized by a discrete Stationary Random Process (independent of the data sequence) with known statistical properties. The purpose of this paper is to characterize the power spectral density (PSD) of baseband signaling schemes in the presence of arbitrary timing jitter. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific results are then given for the cases of practical interest, namely, uniform and Gaussian-distributed jitter. Examples of an uncorrelated data pulse stream, an independent identically distributed data stream, and a Markov source are given. Interesting results emerge when the generating sequence {a/sub n/} is uncorrelated. For generating sequences {a/sub n/} that are nonzero-mean, timing jitter has the effect of widening the main lobe of the spectrum and increasing the sidelobes. When the generating sequence is zero-mean and uncorrelated, a rather surprising result is that the timing jitter does not affect the PSD. Simulation results are also presented to verify the analysis.
Martin Schlather - One of the best experts on this subject based on the ideXlab platform.
-
can any multivariate gaussian vector be interpreted as a sample from a Stationary Random Process
Statistics & Probability Letters, 2007Co-Authors: Olivier Perrin, Martin SchlatherAbstract:We show that a Gaussian Random vector can always be interpreted as a sample from a Stationary Random function on a graph in , d[greater-or-equal, slanted]2, provided that the expectations are the same for all components and the covariance matrix has identical components on the diagonal.
-
can any multivariate gaussian vector be interpreted as a sample from a Stationary Random Process
Statistics & Probability Letters, 2007Co-Authors: Olivier Perrin, Martin SchlatherAbstract:Abstract We show that a Gaussian Random vector can always be interpreted as a sample from a Stationary Random function on a graph in R d , d ⩾ 2 , provided that the expectations are the same for all components and the covariance matrix has identical components on the diagonal.
Abdourrahmane M. Atto - One of the best experts on this subject based on the ideXlab platform.
-
review on the statistical decorrelation of the wavelet packet coefficients of a band limited wide sense Stationary Random Process
Signal Processing, 2007Co-Authors: Abdourrahmane M. Atto, Dominique Pastor, Alexandru IsarAbstract:This paper is a contribution to the analysis of the statistical correlation of the wavelet packet coefficients resulting from the decomposition of a Random Process, Stationary in the wide-sense, whose power spectral density (PSD) is bounded with support in [-@p,@p]. Consider two quadrature mirror filters (QMF) that depend on a parameter r, such that these filters tend almost everywhere to the Shannon QMF when r increases. The parameter r is called the order of the QMF under consideration. The order of the Daubechies filters (resp. the Battle-Lemarie filters) is the number of vanishing moments of the wavelet function (resp. the spline order of the scaling function). Given any decomposition path in the wavelet packet tree, the wavelet packet coefficients are proved to decorrelate for every packet associated with a large enough resolution level, provided that the QMF order is large enough and above a value that depends on this wavelet packet. Another consequence of our derivation is that, when the coefficients associated with a given wavelet packet are approximately decorrelated, the value of the autocorrelation function of these coefficients at lag 0 is close to the value taken by the PSD of the decomposed Process at a specific point. This specific point depends on the path followed in the wavelet packet tree to attain the wavelet packet under consideration. Some simulations highlight the good quality of the ''whitening'' effect that can be obtained in practical cases.
-
On the asymptotic decorrelation of the wavelet packet coefficients of a wide-sense Stationary Random Process
2006Co-Authors: Abdourrahmane M. Atto, Dominique Pastor, Alexandru IsarAbstract:This paper is a contribution to the analysis of the statistic al correla- tion of the wavelet packet coefficients resulting from the dec omposition of a Random Process, Stationary in the wide-sense, whose pow er spectral density is bounded with support in [ − π, π ]. Consider two quadrature mirror filters (QMF) that depend on a pa- rameter r , such that these filters tend almost everywhere to the Shan- non QMF when r increases. The parameter r is called the order of the QMF under consideration. The order of the Daubechies filters (resp. the Battle-Lemari ́e filters) is the number of vanishing moments of the wavelet function (resp. the spline order of the scaling function). Given any decomposition path in the wavelet packet tree, the wavelet packet coefficients are proved to decorrelate for every packe t associated with a large enough resolution level, provided that the QMF o rder is large enough and above a value that depends on this wavelet packet. Another consequence of our derivation is that, when the coeffi cients associated with a given wavelet packet are approximately de correlated, the value of the autocorrelation function of these coefficients a t lag 0 is close to the value taken by the power spectral density of the decompos ed Process at a specific point. This specific point depends on the path fol lowed in the wavelet packet tree to attain the wavelet packet under co nsideration. Some simulations highlight the good quality of the "whiteni ng" effect that can be obtained in practical cases.
M.b. Matthews - One of the best experts on this subject based on the ideXlab platform.
-
On the linear minimum-mean-squared-error estimation of an undersampled wide-sense Stationary Random Process
IEEE Transactions on Signal Processing, 2000Co-Authors: M.b. MatthewsAbstract:We consider the problem of linearly estimating, in the sense of minimum-mean-squared error, a wide-sense Stationary Process in noise given uniformly spaced samples where the sampling interval is such that significant aliasing occurs. We derive the corresponding aliased Wiener filter and provide a technique for determining a closed form for the necessary power spectral density functions. We conclude with an example where both signal and noise are modeled using a second-order innovations representation.
