Statistical methods for investigating phase relations in stationary stochastic processes

Huber, Peter J.; Kleiner, Beat; Gasser, T.; Dumermuth, G

doi:10.1109/tau.1971.1162163

Cited by 182 publications

(59 citation statements)

References 7 publications

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“…With higher order spectral analysis, it is not merely a question of reducing spectral leakage from windowing but understanding the effect that leakage will have on estimates of relevant parameters. Spectral leakage and windowing in the estimation of the bispectrum are discussed in [28,29]. In general, spectral leakage from statistically independent or random phase components will have a similar effect on higher order spectra as the addition of white random noise.…”

Section: Sampling Of Random Processesmentioning

confidence: 99%

Time-varying bispectral analysis of visually evoked multi-channel EEG

Chandran

2012

EURASIP J. Adv. Signal Process.

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Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a nonstationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multichannel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops.The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

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Section: Sampling Of Random Processesmentioning

confidence: 99%

Time-varying bispectral analysis of visually evoked multi-channel EEG

Chandran

2012

EURASIP J. Adv. Signal Process.

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“…On the other hand, methods for estimation of higher order spectra have been much less studied. Methods for estimation of third order spectrum can be found in [85] [86] [69]. Methods for estimation of fourth order spectrum are discussed in [36], [38] and references therein.…”

Section: Estimation Of Fourth Order Spectramentioning

confidence: 99%

Localization of packet based radio transmitters in space, time, and frequency

Ivkovic

Spasojević

Seskar

2008

2008 42nd Asilomar Conference on Signals, Systems and Computers

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We consider the scenario where one or more sensors observe a frequency band potentially used by multiple radio transmitters forming packet based networks. Our goal is to develop algorithms for estimation of spectrum usage in space, time, and frequency. This estimation is obtained by performing some form of analysis of the received signals at the sensors. The proposed algorithms can be used for achieving efficient spectrum utilization by identifying unused portions of spectrum in space, time and frequency as well as for other applications requiring spectrum monitoring.The received signals consist of packets from multiple transmitters with possible timefrequency collisions. Each received signal consists of multiple statistically homogeneous segments where each combination of active transmitted signals creates one or more of such segments. In order to perform any form of statistical analysis using conventional methods for stationary or cyclostationary signals these segments must be first localized in time. In the first part of the thesis we propose a nonparametric algorithm for solving this problem. Initial segmentation is computed using a variant of mean shift algorithm, which is a clustering tool based on nonparametric estimate of the underlying probability distribution. We show that this type of mean shift algorithm is based on the modified Newton's method and provide a convergence analysis which explains how and why ii the algorithm works. Final segmentation results are obtained after applying a cluster validation procedure and impulse noise filtering on the initial segmentation results.In the second part of the thesis we propose a method for analysis of the segments localized in the first step. This method is useful if transmitted signals are linearly modulated or can be approximated as sums of linearly modulated signals. For each set of segments generated by the same combination of the transmitted signals we compute a certain two dimensional slice of the fourth order spectrum. These slices are arranged in a three way array. We show that under certain conditions it is possible to recover contributions of individual signals to the observed three way array by decomposing the array into low rank terms. Thus, for each received signal we can estimate its spectrum and the associated activity sequence in time. We discuss the uniqueness conditions, treat the nontrivial problem of fourth order spectrum estimation and propose a numerical algorithm for estimation of the spectra and the associated activity sequences of individual signals from the observed three way array.The algorithms for segmentation and fourth order spectrum based analysis require only one sensor. In the third part of the thesis we assume that multiple sensors are available. Using the algorithms mentioned above for each transmitter we can estimate its received spectrum at different sensors. From the received spectra of the same transmitted signal at different sensors it is possible to estimate the source signal spectrum and transfer functions of the ch...

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“…In the current work the bispectrum is estimated directly by recording a long signal that is divided into N shorter records labelled n (= 1,2, …, N). The Fourier transform, A n (f), of each record is then calculated and the bispectrum is estimated as A n (f 1 )A n (f 2 )A n * (f 1 +f 2 ) averaged over the N records [12,13]. For a given pair of frequencies f 1 and f 2 there are four conditions for a non-zero bispectrum:…”

Section: The Bispectrummentioning

confidence: 99%

“…Attempts to use these effects to detect cracks have typically concentrated on using the power spectrum to quantify the signals produced by the nonlinear behaviour, although the advantages of the bispectrum in detecting quadratically-phase-coupled signals [5][6][7][8][9] has lead to some interest in using the bispectrum in crack detection [10][11][12][13][14]. As the increase in crack length results in an increase in the bispectrum value corresponding to the mixing frequency [1] that bispectrum value is useful as a measure of the damage.…”

Section: Introductionmentioning

confidence: 99%

Global crack detection using bispectral analysis

et al. 2006

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A global non-destructive testing technique for detecting cracks in engineering parts has been developed. The technique uses the bispectrum to analyse the mixing of two ultrasonic sinusoidal waves in a sample. The bispectrum's insensitivity to noise allows more sensitive detection of mixing signals than the power spectrum. Two sinusoidal signals are generated by signal generators, amplified and applied to a piezo-ceramic disk bonded to a sample. The sample is excited at very-high-order modes of vibration. The response of the sample is measured by a second piezoceramic disk and the received signal analysed using the bispectrum signalprocessing technique. Frequency mixing occurs as a result of the non-linear behaviour of cracks in the structure. Experiments with fatigue-cracked steel beams demonstrate that fatigue cracks produce a strong mixing effect and that the bispectrum signal relating to the frequency mixing is sensitive to the length of the crack; allowing the quantification of the crack length. Progress is being made in applying the technique to more practical situations: the sensitivity of the technique to transducer position and the input signal parameters (frequency and amplitude) is quantified experimentally.

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Statistical methods for investigating phase relations in stationary stochastic processes

Cited by 182 publications

References 7 publications

Time-varying bispectral analysis of visually evoked multi-channel EEG

Time-varying bispectral analysis of visually evoked multi-channel EEG

Localization of packet based radio transmitters in space, time, and frequency

Global crack detection using bispectral analysis

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