Abstract—This paper aims to present a systematic characterisation of the electromyogram (EMG) signal using a nonlinear chaotic approach. EMG signals from 10 muscles in the leg during walking and maximum voluntary contraction (MVC) were obtained and pre-processed using wavelet based denoising techniques. All signals were tested for non-linearity, stationarity and determinism. Chaotic characterization was done by calculating invariants such as correlation dimension (D 2 ), Lyapunov spectrum (λ i ) and Kaplan-Yorke dimension (D KY ). The EMG signals were non-linear and short-term stationary. Determinism and structure was found in the phase- space by studying the recurrence plots. Based on the values of the chaotic invariants, EMG signals were found to exhibit signs of chaotic behaviour with a dimension between 2 and 3 for walking and 3 and 4 for MVC data. Keywords—Chaotic dynamics, Correlation Dimension, EMG, Lyapunov Exponents, Kaplan-Yorke Dimension I. INTRODUCTION An electromyogram (EMG) measures the electrical activity of muscles to gather information about muscular and nervous systems. It is commonly used in diagnosis of muscle weakness or paralysis, muscle or motor problems, sensory problems, nerve damage or injury. EMG also finds use in other fields such as kinesiology, gait and posture studies and prosthesis design [1]. Recent research has focused on single fibre and needle EMG rather than surface EMG (SEMG), even though the latter is more commonly used in practice. SEMG is gaining importance in fields such as physiological muscle assessment, rehabilitation, sport and geriatric medicine and non-invasive evaluation of muscle function and performance. While it is known that interference and muscle cross-talk introduces non-linearity into the signal [2], methods for non-linear time series analysis like phase-space reconstruction, chaotic characterization and non-linear prediction have not been used widely with EMG. Among the few existing studies, there have been conflicting results. The work of Yang et al [3] concludes that EMG exhibits high dimensional chaos, while Small et al [4] fail to find evidence of chaotic behaviour. To the best of our knowledge, not much work has been done to determine the dynamics of EMG. This paper thus aims to present, in a systematic fashion, a complete non-linear analysis of surface EMG signals during walking and in a state of maximum voluntary contraction (MVC). After pre-processing the raw data to remove noise, signal qualification was done using tests for non-linearity and stationarity. This is a necessary step for chaotic characterization, which was then performed by calculating the values of invariants such as D 2 , λ i and D KY . II. SIGNAL DESCRIPTION AND PREPROCESSING The EMG signal is produced as a result of the superposition of a number of motor unit action potential trains. The recorded signal is in effect the sum of these potentials passed through a possibly nonlinear filter made up of muscle tissue, adipose tissue and the skin-air interface. Recording apparatus may also introduce white noise and other artifacts [1], [2]. The surface EMG datasets were obtained from Motion Labs Systems (ML dataset) [5] and Texas University (TU dataset) [6]. Wavelet-based denoising was performed prior to signal analysis to minimize noise. Wavelet denoising has been found to be effective in denoising a number of physiological signals [7]. It is preferred over simple frequency domain filtering because it tends to preserve signal characteristics even while minimizing noise. This is because a number of thresholding strategies are available, allowing reconstruction based on selected detail coefficients [8]. Wavelets commonly used for denoising biosignals include the Daubechies wavelets ‘db2’ and ‘db6’ and the orthogonal Meyer wavelet. We generally tried to choose wavelets whose shapes are similar to those of motor unit action potentials [7]. III. SIGNAL QUALIFICATION A. Test for Non-linearity Most non-linearity tests are done by specifying some well-defined null hypothesis (e.g. that the data is generated by a Gaussian linear stochastic process) and computing a statistic to test against this hypothesis [9]. Since we do not know the distribution of the statistic beforehand, we estimate it using the method of surrogate data. Methods for generating surrogates are described by Theiler et al [10]. We use two of these methods in our study: (i) Phase randomized and (ii) Gaussian scaled surrogates. The first is generated by randomizing the phases of the Fourier transform of the signal and then inverting it to get the time domain signal. The surrogate thus has an identical power spectrum, mean, variance and autocorrelation as the original but has a different distribution of amplitudes Nonlinear Analysis of EMG Signals – A Chaotic Approach Pavitra Padmanabhan and Sadasivan Puthusserypady Department of Electrical and Computer Engineering, National University of Singapore 4 Engineering Drive 3, Singapore – 117576. 0-7803-8439-3/04/$20.00©2004 IEEE 608 Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA • September 1-5, 2004