Sharp Wave Based HHT Time-frequency Features with Transmission Error

Abstract

Signal analysis is a field of study that attempts to extract information features from various physical phenomena. Fourier transform (FT), wavelet transform (WT), and Hilbert-Huang transformation (HHT) are the 3 major approaches used in signal analysis (Huang et al., 1998) (Yan & Gao, 2007). FT is a global energy-frequency distribution approach that is suitable for analyzing linear, strictly periodic, and stationary signals. In contrast, HHT is a good method for analyzing non-linear and non-stationary signals, such as those associated with wind, earthquakes, electrocardiographs (ECGs), and electroencephalograms (EEGs). This method can also used to describe the local features of dynamic signals, and illustrate the energy-frequency-time distribution of these signals. The 2 principal steps employed in HHT are empirical mode decomposition (EMD) and Hilbert spectral analysis, EMD is used to decompose local signals to finite data sets, which are referred to as intrinsic mode functions (IMFs), and Hilbert transforms (HTs) are used in conjunction with the obtained IMFs to determine the instantaneous frequencies (IFs), time-frequency-energy distributions of the local time signals. A number of studies have been performed to elucidate various aspects of signal analysis. Cohen reviewed the fundamental ideas, methods, and characteristics of the time-frequency analysis approaches employed until 1989 (Cohen, 1989). Blanco et al., used the Gabor transform (GT) time-frequency analysis approach to facilitate identification of the source of epileptic seizures (Blanco et al., 1997). The GT approach is similar to the fast FT approach, but GT offers the advantage of allowing the analysis of the frequencies and their time evolution. Blanco et al., adopted GT to achieve maximal concentration of the time and frequency characteristics for epilepsy and obtain accurate information on the time evolution of the frequency epileptic activity. Tzallas et al., used short-time Fourier transform and 12 different time-frequency distributions for studying epilepsy classification problems and discussed the obtained sensitivity, accuracy, and selectivity results, and the characteristic data features for the detection of epilepsy (Tzallas et al., 2009). However, they did not use the HHT-based time-frequency analysis approach to define epileptic sharps. Sharabaty et al., used the HHT signal-analysis approach to determine the alpha and theta localizations for estimation of the vigilance level, and