Nonlinear denoising of transient signals with application to event related potentials

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres

Thermal diagnostic of the Optical Window on board LISA Pathfinder

Vacuum conditions inside the LTP Gravitational Reference Sensor must comply with rather demanding requirements. The Optical Window (OW) is an interface which seals the vacuum enclosure and, at the same time, lets the laser beam go through for interferometric Metrology with the test masses. The OW is a plane-parallel plate clamped in a Titanium flange, and is considerably sensitive to thermal and stress fluctuations. It is critical for the required precision measurements, hence its temperature will be carefully monitored in flight. This paper reports on the results of a series of OW characterisation laboratory runs, intended to study its response to selected thermal signals, as well as their fit to numerical models, and the meaning of the latter. We find that a single pole ARMA transfer function provides a consistent approximation to the OW response to thermal excitations, and derive a relationship with the physical processes taking place in the OW. We also show how system noise reduction can be accomplished by means of that transfer function.Comment: 20 pages, 14 figures; accepted for publication in Class. Quantum Gra

Multiple Local Whittle Estimation in StationarySystems

Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (?), at the frequency of principal interest, zero; for shortmemory series ? = 0 automatically. The latter case has also been stressed under longmemory, along with the 'fractional differencing' case ( ) / 2; 2 1 ? = d - d p where 1 2 d , dare the memory parameters of the two series. We develop time domain conditionsunder which these are and are not relevant, and relate the consequent properties ofcross-autocovariances to ones of the (possibly bilateral) moving averagerepresentation which, with martingale difference innovations of arbitrary dimension,is used in asymptotic theory for local Whittle parameter estimates depending on asingle smoothing number. Incorporating also a regression parameter (ß) which, whennon-zero, indicates cointegration, the consistency proof of these implicitly-definedestimates is nonstandard due to the ß estimate converging faster than the others. Wealso establish joint asymptotic normality of the estimates, and indicate how thisoutcome can apply in statistical inference on several questions of interest. Issues ofimplementation are discussed, along with implications of knowing ß and of correct orincorrect specification of ? , and possible extensions to higher-dimensional systemsand nonstationary series.Long memory, phase, cointegration, semiparametricestimation, consistency, asymptotic normality.

The detection of freezing of gait in Parkinson's disease using asymmetric basis function TV-ARMA time-frequency spectral estimation method

Freezing of gait (FOG) is an episodic gait disturbance affecting locomotion in Parkinson’s disease. As a biomarker to detect FOG, the Freeze index (FI), which is defined as the ratio of the areas under power spectra in ‘freeze’ band and in ‘locomotion’ band, can negatively be affected by poor time and frequency resolution of time-frequency spectrum estimate when short-time Fourier transform (STFT) or Wavelet transform (WT) is used. In this study, a novel high-resolution parametric time-frequency spectral estimation method is proposed to improve the accuracy of FI. A time-varying autoregressive moving average model (TV-ARMA) is first identified where the time-varying parameters are estimated using an asymmetric basis function expansion method. The TV-ARMA model is then transformed into frequency domain to estimate the time-frequency spectrum and calculate the FI. Results evaluated on the Daphnet Freezing of Gait Dataset show that the new method improves the time and frequency resolutions of the time-frequency spectrum and the associate FI has better performance in the detection of FOG than its counterparts based on STFT and WT methods do. Moreover, FOGs can be predicted in advance of its occurrence in most cases using the new method

Analysis of the structure of time-frequency information in electromagnetic brain signals

This thesis encompasses methodological developments and experimental work aimed at revealing information contained in time, frequency, and time–frequency representations of electromagnetic, specifically magnetoencephalographic, brain signals. The work can be divided into six endeavors. First, it was shown that sound slopes increasing in intensity from undetectable to audible elicit event-related responses (ERRs) that predict behavioral sound detection. This provides an opportunity to use non-invasive brain measures in hearing assessment. Second, the actively debated generation mechanism of ERRs was examined using novel analysis techniques, which showed that auditory stimulation did not result in phase reorganization of ongoing neural oscillations, and that processes additive to the oscillations accounted for the generation of ERRs. Third, the prerequisites for the use of continuous wavelet transform in the interrogation of event-related brain processes were established. Subsequently, it was found that auditory stimulation resulted in an intermittent dampening of ongoing oscillations. Fourth, information on the time–frequency structure of ERRs was used to reveal that, depending on measurement condition, amplitude differences in averaged ERRs were due to changes in temporal alignment or in amplitudes of the single-trial ERRs. Fifth, a method that exploits mutual information of spectral estimates obtained with several window lengths was introduced. It allows the removal of frequency-dependent noise slopes and the accentuation of spectral peaks. Finally, a two-dimensional statistical data representation was developed, wherein all frequency components of a signal are made directly comparable according to spectral distribution of their envelope modulations by using the fractal property of the wavelet transform. This representation reveals noise buried processes and describes their envelope behavior. These examinations provide for two general conjectures. The stability of structures, or the level of stationarity, in a signal determines the appropriate analysis method and can be used as a measure to reveal processes that may not be observable with other available analysis approaches. The results also indicate that transient neural activity, reflected in ERRs, is a viable means of representing information in the human brain.reviewe

Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory

Nonlinear functions of multivariate financial time series can exhibit longmemory and fractional cointegration. However, tools for analysingthese phenomena have principally been justified under assumptionsthat are invalid in this setting. Determination of asymptotic theoryunder more plausible assumptions can be complicated and lengthy.We discuss these issues and present a Monte Carlo study, showingthat asymptotic theory should not necessarily be expected to provide agood approximation to finite-sample behaviour.Fractional cointegration, memory estimation,stochastic volatility.