Multi-scale phase average waveform of electroencephalogram signals in childhood absence epilepsy using wavelet transformation

BACKGROUND： Recent studies have focused on various methods of wavelet transformation for electroencephalogram （EEG） signals. However, there are very few studies reporting characteristics of multi-scale phase waves during epileptic discharge.OBJECTIVE： To extract multi-scale phase average waveforms from childhood absence epilepsy EEG signals between time and frequency domains using wavelet transformation, and to compare EEG signals of absence seizure with pre-epileptic seizure and normal children, and to quantify multi-scale phase average waveforms from childhood absence epilepsy EEG signals. DESIGN, TIME AND SETTING： The case-comparative experiment was performed at the Department of Neuroelectrophysiology, Tianjin Medical University from August 2002 to May 2005. PARTICIPANTS： A total of 15 patients with childhood absence epilepsy from the General Hospital of Tianjin Medical University were enrolled in the study. The patients were not administered anti-epileptic drugs or sedatives prior to EEG testing. In addition, 12 healthy, age- and gender-matched children were also enrolled.METHODS： EEG signals were tested on 15 patients with childhood absence epilepsy and 12 normal children. Epileptic discharge signals during clinical and subclinical seizures were collected 10 and 20 times, respectively. The collected EEG signals were treated with wavelet transformation to extract multi-scale characteristics during absence epilepsy seizure using a conditional sampling method. Multi-scale phase average waveforms were collected using a conditional phase averaging technique. Amplitude of phase average waveform from EEG signals of epilepsy seizure, subclinical epileptic discharge, and EEG signals of normal children were compared and statistically analyzed in the first half-cycle.MAIN OUTCOME MEASURES： Multi-scale wavelet coefficient and the evolution of EEG signals were observed during childhood absence epilepsy seizures using wavelet transformation. Multi-scale phase average waveforms from EEG signals were observed using a conditional sampling method and phase averaging technique.RESULTS： Multi-scale characteristics of EEG signals demonstrated that 12-scale （3 Hz） rhythmical activity was significantly enhanced during childhood absence epilepsy seizure and co-existed with background structure （〈1 Hz, low frequency discharge）. The phase average wave exhibited opposed phase abnormal rhythm at 3 Hz. Prior to childhood absence epilepsy seizure, EEG detected opposed abnormal a rhythm and 3 Hz composition, which were not detected with traditional EEG. Compared to EEG signals from normal children, epileptic discharges from clinical and subclinical childhood absence epilepsy seizures were positive and amplitude was significantly greater （P〈0.05）.CONCLUSION： Wavelet transformation was used to analyze EEG signals from childhood absence epilepsy to obtain multi-scale quantitative characteristics and phase average waveforms. Multi-scale wavelet coefficients of EEG signals correlated with childhood absence epilepsy seizure, and multi-scale waveforms prior to epilepsy seizure were similar to characteristics during the onset period. Compared to normal children, EEG signals during epilepsy seizure exhibited an opposed phase model.

Modified Approach to PGA Phase Averaging for ISAR Autofocus

A new approach to phase averaging in phase gradient algorithm (PGA) is proposed, which is based on the fundamental fact that the information of translational phase error is widely contained in every defocused scatterer in ISAR image. The new approach aims to choose strong scatterers for error phase averaging with a threshold rather than just simply to pick out the strongest point in each range cell, which is not necessarily real strong scatterers if in some range cells consists more than one strong scatterer and whereas in other range cells no scatterer at all. The results of processing real data are presented to confirm the validity of the proposed approach.

Improving coherent averaging line spectrum detection with phase interpolation and compensation

For the purpose of resolving the problem of performance deterioration introduced by inaccurate phase compensation in existing coherent averaging line spectrum detectors, a modified coherent detector is proposed. The three point interpolation in frequency domain is applied to obtain accurate estimate of phase difference between segments when the segmented length is not an integral multiple of the signal period. Then the segmented data are multiplied by a complex coefficient to remove the phase difference and synchronize the phases of all the segments before coherent averaging. Theoretical analysis shows that there will be a gain of 3.9 dB at most by using the modified detector. The detection performance of the incoher- ent averaging power spectrum detector （AVGPR）, the phase coherent averaging detector, the modified coherent averaging detector are compared with each other by computer simulations. The results coincide basically with the theoretical analysis, which show the superiority of the modified detector to the former two detectors.

CONDITIONAL AVERAGING OF TR-PIV MEASUREMENTS OF WAKE BEHIND SQUARE CYLINDER USING AN IMPROVED CROSS-CORRELATION APPROACH

An improved phase averaging method based on cross-correlation of the instantaneous velocity field determined by TR-PIV measurements is proposed in this article. A Time-Resolved Particle Image Velocimetry （TR-PIV） is used to measure the two-dimensional wake behind the square cylinder. The phase signals associated with the deterministic appearance of the Karman vortex street are obtained by calculating the correlation matrix of the low-pass filtered velocity field, and can provide the complete information of the phase-averaged wake flow. The results show the advantages of the enhanced methodology in extracting the quasi-periodic flow patterns related to the shedding coherent structures without using additional reference signals.