The Estimation of the Instantaneous Amplitudes and the Instantaneous Frequencies of the EEG when both are Stochastic Processes

Abstract: Abstract: In this report we model the EEG signal as a sum of sine waves. Each sine wave has a random frequency and a random amplitude. We use band pass filters to separate the different frequency segments of the EEG. The frequency is modeled as an Ornstein-Uhlenbeck (OU) stochastic process i.e. the frequency is bouncing around a mean value. In each EEG band, an adaptive filter is developed to estimate the random frequency. The instantaneous amplitude is then obtained by using adaptive noise cancelling where one channel is the EEG band pass signal and the other channel is the estimated sine wave with random frequency. Another amplitude estimate is obtained by using energy separation operator with the estimated frequency. The results are compared to the Teager energy separation operator (TEO) and showed better performance.