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Bayesian Spectrum Estimation of Unevenly Sampled Nonstationary Data
 Proceedings of the International Conference on Acoustics Speech and Signal Processing
, 2002
"... Spectral estimation methods typically assume stationarity and uniform spacing between samples of data. The nonstationarity of real data is usually accommodated by windowing methods, while the lack of uniformlyspaced samples is typically addressed by methods that "fill in" the data in some way. Thi ..."
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Cited by 17 (1 self)
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Spectral estimation methods typically assume stationarity and uniform spacing between samples of data. The nonstationarity of real data is usually accommodated by windowing methods, while the lack of uniformlyspaced samples is typically addressed by methods that "fill in" the data in some way. This paper presents a new approach to both of these problems: we use a Bayesian framework, which includes a nonstationary Kalman filter, to jointly estimate all spectral coe#cients instantaneously. The new method works regardless whether the samples are evenly or unevenly spaced; moreover, it provides a new approach to enabling processing when it is desirable to virtually eliminate aliasing by unevenly sampling. An amplitudepreservation property of the new method can be used to detect if aliasing occurred. Finally, we propose an e#cient algorithm for sparsifying the spectrum estimates when we know a priori that the signal is narrowband in the frequency domain. We illustrate the new method on several data sets, showing that it can perform well on unevenly sampled nonstationary signals without the use of any sliding window, that it can estimate frequency components beyond half of the average sampling frequency when the signal is unevenly sampled, and that it can provide more accurate estimation than several other important recent and classical methods.
Multitaper timefrequency reassignment for nonstationary spectrum estimation and chirp enhancement
 IEEE Transactions on Signal Processing
"... Abstract—A method is proposed for obtaining timefrequency distributions of chirp signals embedded in nonstationary noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise. The technique consists in combining t ..."
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Cited by 8 (2 self)
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Abstract—A method is proposed for obtaining timefrequency distributions of chirp signals embedded in nonstationary noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise. The technique consists in combining timefrequency reassignment with multitapering, and two variations are proposed. The first one, primarily aimed at nonstationary spectrum estimation, is based on sums of estimates with different tapers, whereas the second one makes use of differences between the same estimates for the sake of chirp enhancement. The principle of the technique is outlined, its implementation based on Hermite functions is justified and discussed, and some examples are provided for supporting the efficiency of the approach, both qualitatively and quantitatively. Index Terms—Chirps, multitapers, reassignment, timefrequency. I.
Testing stationarity with surrogates: A timefrequency approach,” submitted to
 IEEE Trans. Signal Processing
, 2009
"... Abstract — An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local timefrequency features. The originality is to make use of a family of st ..."
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Cited by 5 (2 self)
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Abstract — An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local timefrequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a oneclass classifier, the timefrequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.
Testing stationarity with surrogates — A oneclass SVM approach
 in Proc. IEEE Stat. Sig. Proc. Workshop SSP07, Madison (WI
"... An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local timefrequency features. The originality is to make use of a family of stationary su ..."
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Cited by 4 (3 self)
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An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local timefrequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis and to base on them a statistical test implemented as a oneclass Support Vector Machine. The timefrequency features extracted from the surrogates are considered as a learning set and used to detect departure from stationnarity. The principle of the method is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.
A note on reassigned Gabor spectrograms of Hermite functions
, 2012
"... An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limited by the “classical ” circle where the Gabor spectrogram attains its maximum value, with ..."
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An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limited by the “classical ” circle where the Gabor spectrogram attains its maximum value, with a perfect localization that can only be achieved in the limit of infinite order. 1