The bispectrum of complex signals: definitions and properties

The symmetry properties and the relationship between all forms of third-order cumulants of complex signals are investigated. It is shown that all cumulants (for different position of the complex conjugate) are related by simple transformations. Autoregressive modeling of complex-valued signals using third-order cumulants is also investigated. It is shown that modeling of complex-valued signals requires a different approach from modeling of real-valued signals     

Bispectra of modulated stationary signals

Complex modulation affects the bispectral signatures of a random process and complicates the interpretation of the bispectrum. The impact of complex modulation on bispectral signature analysis and on the detection performance of multitone signals is examined     

Cortisol secretion is related to electroencephalographic alertness in human subjects during daytime wakefulness

To determine whether human hypothalamo-pituitary-adrenal axis activity is related to the alertness level during wakefulness, 10 healthy young men were studied under resting conditions in the daytime (0900-1800 h) after an 8-h nighttime sleep (2300-0700 h). A serial 70-sec gaze fixation task was required every 10 min throughout the daytime experimental session. The corresponding waking electroencephalographic (EEG) segments were submitted to quantitative spectral analysis, from which EEG beta activity (absolute power density in the 13-35 Hz frequency band), an index of central alertness, was computed. Blood was collected continuously through an indwelling venous catheter and sampled at 10-min intervals. Plasma cortisol concentrations were measured by RIA, and the corresponding secretory rates were determined by a deconvolution procedure. Analysis of individual profiles demonstrated a declining tendency for EEG beta activity and cortisol secretory rate, with an overall temporal relationship indicated by positive and significant cross-correlation coefficients between the two variables in all subjects (average r=0.565, P < 0.001). Changes in cortisol secretion lagged behind fluctuations in EEG beta activity, with an average delay of 10 min for all the subjects. On the average, 4.6+/-0.4 cortisol secretory pulses and 4.9+/-0.5 peaks in EEG beta activity were identified by a detection algorithm. A significant, although not systematic, association between the episodes in the two variables was found: 44% of the peaks in EEG beta activity (relative amplitude, near 125%; P < 0.001) occurred during an ascending phase of cortisol secretion, cortisol secretory rates increasing by 40% (P < 0.01) 10-min after peaks in EEG beta activity. However, no significant change in EEG beta activity was observed during the period from 50 min before to 50 min after pulses in cortisol secretion. In conclusion, the present study describes a temporal coupling between cortisol release and central alertness, as reflected in the waking EEG beta activity. These findings suggest the existence of connections between the mechanisms involved in the control of hypothalamo-pituitary-adrenal activity and the activation processes of the brain, which undergoes varying degrees of alertness throughout daytime wakefulness.     

Human ECoG analysis during speech perception using matching pursuit: a comparison between stochastic and dyadic dictionaries

We use the matching pursuit (MP) algorithm to detect induced gamma activity in human EEG during speech perception. We show that the MP algorithm is particularly useful for detecting small power changes at high gamma frequencies (> 70 Hz). We also compare the performance of the MP using a stochastic versus a dyadic dictionary and show that despite the frequency bias the time-frequency power plot (averaged over 100 trials) generated by the dyadic MP is almost identical (> 98.5%) to the one generated by the stochastic MP. However, the dyadic MP is computationally much faster than the stochastic MP.