1780 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 10, OCTOBER 2007 Describing the Nonstationarity Level of Neurological Signals Based on Quantifications of Time–Frequency Representation Shanbao Tong*, Member, IEEE, Zhengjun Li, Yisheng Zhu, Senior Member, IEEE, and Nitish V. Thakor, Fellow, IEEE Abstract—Most neurological signals including electroencephalo- gram (EEG), evoked potential (EP) and local field potential (LFP) have been known to be time varying and nonstationary, especially in some pathological conditions. Currently, the most widely used quantitative tool for such nonstationary signals is time–frequency representation (TFR) which demonstrates the temporal evolution of different frequency components. However, TFR does not directly provide a quantitative measure of nonstationarity level, e.g., how far the process deviates from stationarity. In this study, we intro- duced three different quantifications of TFR (qTFR) to charac- terize the nonstationarity level of the involving signals: 1) degree of stationarity (DS); 2) Shannon entropy (SE) of the marginal spec- trum; and 3) Kullback–Leibler distance (KLD) between a TFR and a uniform distribution. These descriptors provide quantita- tive analysis of stationarity of a signal such that the stationarity of different signals could be compared. In this study, we obtained the TFRs of the EEG signals before and after the hypoxic-ischemic (HI) brain injury and examined the stationarity of the EEG. DS, SE, and KLD can indicate the nonstationarity change of EEG at each frequency following the HI injury, especially in the upper -and lower -band (e.g., Hz Hz ) as well as in the band (e.g., 22 Hz-26 Hz ). Moreover, it is shown that the stationarity of the EEG changes differently in different frequencies following the HI injury. Index Terms—Electroencephalogram (EEG), Kullback–Leibler distance, Shannon entropy, stationarity, time–frequency represen- tation (TFR). I. INTRODUCTION E LECTRO-NEUROLOGICAL signals such as electroen- cephalogram (EEG), event-related potential(ERP) and local field potential (LFP) record the excitory level of neural activities. Due to the intrinsic time-varying properties of the neural system, neurological signals have been regarded as nonstationary waveforms in a relative large time scale [1], [2]. By far, the most widely used quantitative EEG (qEEG) analysis is spectra-based frequency analysis, which assumes that the Manuscript received July 1, 2006; revised December 11, 2006. This work was supported in part by the NSFC under Grants 60601012 and 60671058, FANEDD and the fundingof Shanghai Jiao Tong University for Young Faculties. N.V.T. is also supported by the NIH under Grant 1RO1HL71568. Asterisk indicates corresponding author. *S. Tong is with the Biomedical Engineering Department, Shanghai Jiao Tong University, Jiao Yi Lou Building, Room 411, 1954 Huashan Road, Shanghai, 200240, China (e-mail: shanbao.tong@gmail.com). Z. Li and Y. Zhu are with the Biomedical Engineering Department, Shanghai Jiao Tong University, Shanghai, 200240, China. N. V. Thakor is with the Biomedical Engineering Department, Johns Hopkins School of Medicine, Baltimore, MD 21205 USA. Digital Object Identifier 10.1109/TBME.2007.893497 signal is stationary. Sometimes we need to localize the transient neural activities, such as epileptic seizure, spikes, spindling, and bursting in EEG, and we have to resort to the nonstationary analysis tools, e.g., time–frequency representation (TFR). The principle of TFR is to extract the energy distribution on a time versus frequency plane so that different frequency components can be localized at a good temporal resolution. Although TFR provides a 2-D visualization of the energy distribution of a signal, it does not directly show the stationarity difference between two TFRs. In some neurophysiological studies, it is desirable to compare the stationarity at specific frequencies [3], [4]. We have proposed a measure, called time–frequency complexity , as a stationarity index to quantify how much the EEG is uniformly distributed on the time–frequency plane [5] TFC (1) where is the TFR of EEG. The advantage of TFC is that it provides a simple scalar nonstationarity index. Never- theless, TFC is not able to differentiate whether the nonunifor- mity is from time or the frequency domain. Huang proposed a measure, named degree of stationarity (DS), in Hilbert–Huang transform (HHT) [6] DS (2) where is the Hilbert spectra of the empirical mode decomposition (EMD) of a signal, and is the marginal frequency distribution, e.g., . DS is rather powerful when the signal is intrinsically composed of empirical components [6]. Since EMD itself can be affected by high-frequency fluctuations or low-frequency drifting, DS based on HHT is less reliable when the signals are contaminated with noises of bursting activities. In neurological signal processing, we are often interested in the nonstationarity of different rhythms or specific spectral com- ponents [4]. The definition of TFC is too abstract to be asso- ciated with the rhythmic properties. Therefore, in this paper, we will look into defining the stationarity at each frequency. 0018-9294/$25.00 © 2007 IEEE