Frequency Analysis of EMG Signals of Individuals with Spinal Cord Injury: Comparison Between FFT, STFT and Wavelet Methods

Introduction: Surface or wired electromyogram (EMG) signals from skeletal muscles of individuals with spinal cord injury (SCI) have been used to characterize muscle activation during the performance of various motor tasks. Transforming the EMG signal to frequency domain provides information about the frequency content of the signal. Fast Fourier transform (FFT) has been traditionally used to analyze EMG signals in frequency domain. However, FFT has issues such as assuming stationarity for the EMG signal and not being localized in time, so that it is not suited for representing efficiently abrupt changes in the signal. The short-time Fourier transform (STFT) was designed to increase the time resolution of FFT by selecting a fixed-size moving window and take the FFT for each segment; however, STFT may have poor resolution in time and/or frequency domains, depending on the window size. Continuous Wavelet transform (CWT) has been designed to overcome these limitations by being well-localized in time and frequency, representing accurately abrupt signal fluctuations. In this work, we are comparing the results of these three methods for analyzing the EMG signals and present the limitations of each method. Materials and Methods: SCI participants that have been implanted with a spinal cord epidural stimulation (ES) unit in order to modulate the excitability of lumbosacral spinal circuits, performed standing with and without stimulation. EMG signals were recorded from 16 leg muscles (8 muscles on each side) during standing. EMG signals related to stable standing conditions were divided into 10-second time intervals in order to obtain overall stationary signals, and FFT, STFT and CWT (Morlet wavelet) analyses were performed. The power spectral density (PSD), spectrogram and scalogram of the signals were calculated by taking the squared magnitude of FFT, STFT and CWT, respectively. By assuming the wide-sense stationarity, we calculated the mean spectral power values over the selected intervals for each frequency component for STFT and CWT. For a better visual comparison, the spectral power values were normalized to the highest values between these three methods. Results and Discussion: Power spectral values as a function of frequency calculated for EMG signals related to active and inactive muscles with and without ES are shown in Fig. 1. In the cases of EMG signals with muscle activity without ES (Fig.1 top-left), the mean frequency (MNF) values for FFT, STFT and CWT are 130.9 Hz, 131.2 Hz and 133.0 Hz respectively. This shows that CWT is more sensitive in describing high frequency contents of the muscle activation. In the case of muscles contracting with the help of ES, FFT and STFT predominantly present the spikes related to the ES frequency (20 Hz) and its harmonics, and disregard the frequency contents of motor evoked potentials. On the other hand, CWT is able to capture the continuous changes in frequency content of the ES induced evoked potentials that are the building blocks of the recorded EMG and the cause of muscle contraction. When the muscles are not active (with or without ES), noise is recorded from EMG electrodes. In this case, the CWT method shows that the signal power at higher frequencies (>350 Hz) is much greater than at lower frequencies. This finding is substantially different from the results of the two other methods, and suggests that wavelet analysis has the highest sensitivity to abrupt changes (i.e. noise) and it can discriminate between a signal that carries actual muscle response and noise. Conclusion: The differences that are presented in the results (and our calculations) indicate that the features that are commonly calculated in the frequency domain such as mean, median and dominant frequencies and total power are considerably different values for CWT compared to the other two methods. This suggests that specially for ES-evoked muscle responses, even if the signal could be considered stationary, wavelet provides a more accurate representation of the signal frequency components than FFT and STFT.