Intensity analysis in time-frequency space of surface myoelectric signals by wavelets of specified resolution

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Abstract

Surface myoelectric signals often appear to carry more information than what is resolved in root mean square analysis of the progress curves or in its power spectrum. Time-frequency analysis of myoelectric signals has not yet led to satisfactory results in respect of separating simultaneous events in time and frequency. In this study a time-frequency analysis of the intensities in time series was developed. This intensity analysis uses a filter bank of non-linearly scaled wavelets with specified time-resolution to extract time-frequency aspects of the signal. Special procedures were developed to calculate intensity in such a way as to approximate the power of the signal in time. Applied to an EMG signal the intensity analysis was called a functional EMG analysis. The method resolves events within the EMG signal. The time when the events occur and their intensity and frequency distribution are well resolved in the intensity patterns extracted from the EMG signal. Averaging intensity patterns from multiple experiments resolve repeatable functional aspects of muscle activation. Various properties of the functional EMG analysis were shown and discussed using model EMG data and real EMG data.

Introduction

The myoelectric signal, recorded as electromyogram EMG contains valuable information with respect to timing of muscles, the force/EMG signal relationship and the use of the EMG signal as fatigue index [6]. Although many artifacts limit the use of surface electromyography in biomechanics this technique remains an invaluable tool. The means for processing EMG signals for amplitude and spectral analysis seem to be established [6]. For the analysis of the amplitude, usually rectified signals or root mean squared values were used. The frequency content of an EMG signal was analyzed using the Fourier transform and the signal in frequency space can be discussed. The Fourier transform requires recording of the EMG signal over a substantial time period and thus the temporal aspect of the signal collapsed. Shortening of the time interval leads to the windowed Fourier transform with its disadvantages [9], [12]. The main disadvantage results from the fact that a rectangular window either in time or in frequency space becomes part of the transformed signal. The result includes a relatively arbitrary selection of various frequencies out of the Fourier transformed signal or an averaging of signals over a wide spread time interval. The way to cope with these difficulties is to control the shape of the windows as e.g. by using Gauss shaped windows. An alternative approach to define intensities in time and frequency was given by the Wigner–Ville transform [12:104–108] and was successfully used to assess muscle fatigue during dynamic contractions [10]. The muscle fatigue resulted in a decrease of the instantaneous mean frequency. This change in frequency was attributed to a reduction of the velocity of propagation of depolarization along the muscle fibers [10], [2]. The effect was observed with a very low time-resolution compared to body movements. Similar methods would be required that resolve the patterns of myoelectric signal in much shorter time ranges. Furthermore the Wigner–Ville transform was not well suited when applied to multi component signals [10]. A time-frequency analysis based on wavelets is probably a more appropriate tool for such an approach [13]. Wavelet analysis has already found many applications in medicine and biology [1]. The multi-resolution analysis brought great improvements processing images. Especially, denoising processes became very important and were applied to EMG data [3]. Denoising does not yield additional information of the distributions in frequencies within the EMG signal. To obtain detailed time-frequency related information about the myoelectric signal, discrete wavelet analysis was used studying fatigue of muscles and measurements from high jumps under altered-G conditions [4], [5]. The results showed frequency variations but the events contained frequencies covering the whole frequency range and no discrimination was possible. Similar decompositions are important in the analysis of EEG data and can isolate the frequency patterns representing different states of the brain [1:372]. A multi-resolution analysis is optimal if one does not know the time-resolution to be applied to the problem or if detailed shapes of an EMG pulse were to be characterized [7]. For the surface EMG signal this was not the case.

Time-resolution is essential for the analysis of EMG signals. However, time-resolution has to be of the order of the physiological response time of the muscle. Within this physiological response time, especially at high frequencies there is more than one oscillation of the EMG signal that is part of the muscle activation at that moment in time. This led to the concept of an event-oriented intensity analysis. An event could be visualized as a short burst of oscillations with a specific frequency distribution representing the underlying processes. A typical time period for an event should be within times relevant to fast physiological responses. Based on reactions observed during vertical jumps or by unintended activation of muscles [15], [11], time periods of such events were estimated to be between 10 ms and 100 ms. Thus an event lasting 25 ms that appears at a frequency of 200 Hz contains five or more cycles whereas one of 10 ms only contains two cycles. A decomposition of the signal into events requires a time resolution sufficiently short to resolve these events. The time- resolution in this case represents the time required between two events to resolve them as separate ones.

The purpose of this study was to develop a time-frequency analysis resolving events in the EMG signal considering the following:

  • 1.

    Events will be resolved measuring their intensity.

  • 2.

    The intensity will be resolved simultaneously in time and frequency.

  • 3.

    The onset, duration and magnitude of an event will then be determined from the progress of the intensity of the event at the respective frequencies.

  • 4.

    The intensity spectrum will be developed to measure the frequency pattern of an event.

  • 5.

    Events will be resolved with a finite time resolution adapted to physiological functions of the myoelectric signal.

  • 6.

    A newly developed filter-bank of wavelets will be proposed to achieve the intensity measurements of the above points.

  • 7.

    EMG-signals obtained while cycling will be used as practical example.

The concept of intensity represents a quantitative analysis that approximates the power of the EMG signal at time t. The intensity yields the timing and the strength of the event of muscle activation at various frequencies. Events with intensities that occur at one frequency can then be compared with those occurring at other ones. Many valuable approximations are currently used for various tasks. [1]. The presented solution differs from others by the constraint that results from physiological limitations. The events in EMG signals were to be resolved with specified time-resolutions that are much shorter than those currently used. Once such events can be measured, the timing of muscle activation in biomechanical studies can greatly be improved.

Section snippets

Outline of ideas used to achieve the goal of an intensity analysis of events

  • 1.

    Time-resolution was to be adjusted to a range appropriate to the time period of events in the EMG signal. This could be achieved by non-linear scaling of the wavelets but not by the linear scaling as used in multi-resolution analysis. Thus the classical wavelet analysis using linear scaling of a mother wavelet was not further considered. A filter-bank was proposed that consisted of wavelets that were non-linearly scaled and can easily be applied to decompose the intensity from EMG signals into

The simulated model EMG data

Simulated EMG data resembling those expected from measurements made by two surface electrodes in a setup using differential amplifiers for the recording of the EMG signal were generated mimicking muscle activation recorded by surface electrodes. In the present model a pulse generated by a single action potential was approximated by a Gauss curve followed by an inverted one. The width of the Gauss curve was half the electrode diameter divided by the propagation velocity. The time-delay between

Analysis of intensity of sinusoidal data to assess the meaning of time-resolution and intensity

Six sets of data were superimposed to form the signal for the intensity analysis. The superimposed parts of the signal were four sine waves that were switched on in certain time-windows only and two Gabor atoms, sine waves that were amplitude modulated by a Gauss function. The signal thus consisted of:

  • 1.

    Window 1: wave of 40 Hz and amplitude 3 extending from 50 to 375 ms

  • 2.

    Window 2: wave of 170 Hz and amplitude 3 extending from 130 to 170 ms

  • 3.

    Window 3: wave of 60 Hz and amplitude 3 extending from 400

Discussion

The present work revealed the efficacy of a set of specified resolution wavelets in intensity analysis of an EMG signal or any other time-series with limited time-resolution. A separation of the intensities relating to events became possible as well frequency wise as time wise within the limits of bandwidth and time-resolution. The present method offers possibilities to consciously optimize the analysis with respect to time- and frequency-resolution respecting the limits given by the

Acknowledgements

This work was supported by the Swiss National Science Foundation Grant 4034–049857.

Vinzenz von Tscharner was born in Switzerland in 1947. He received his diploma in applied physics and mathematics in 1974 and his PhD degree in biophysics at the University of Basel, Switzerland. He was a post doctorate fellow at Oxford University, in the Depatment of Biochemistry, England in 1978 and 1979, and a post doctorate fellow at Stanford University, California, USA in the Department of Biochemistry in 1998. He returned to the Biocenter in Basel in 1981. He was then research affiliate

References (20)

  • S Conforto et al.

    Optimal rejection of movement artefacts from myoelectric signals by means of a wavelet filtering procedure

    J. Electromyography Kinesiol.

    (1999)
  • A.R Ismail et al.

    Discrete wavelet transform: a tool in smoothing kinematic data

    J. Biomechan.

    (1999)
  • A Aldroubi et al.

    Wavelets in medicine and biology

    (1996)
  • L.R Brody et al.

    pH induced effects on median frequency and conduction velocity on the myoelectric signal

    J. Appl. Physiol.

    (1991)
  • R Constable et al.

    Using the discrete wavelet transform for time-frequency analysis of the surface EMG signal

    Biomed. Sci. Inst.

    (1993)
  • R Constable et al.

    Time-frequency analysis of surface EMG during maximum height jumps under altered-G conditions

    Biomed. Sci. Inst.

    (1994)
  • J DeLuca Carlo

    The use of surface electromyography in biomechanics

    J. Appl. Biomechan.

    (1997)
  • J Fang et al.

    Decomposition of multiunit electromyographic signals

    IEEE Trans. Biomed. Engng.

    (1999)
  • G Kaiser

    A friendly guide to wavelets

    (1994)
  • M Knafliz et al.

    Time-frequency method applied to muscle fatigue assessment during dynamic contractions

    J. Electromyography Kinesiol.

    (1999)
There are more references available in the full text version of this article.

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Vinzenz von Tscharner was born in Switzerland in 1947. He received his diploma in applied physics and mathematics in 1974 and his PhD degree in biophysics at the University of Basel, Switzerland. He was a post doctorate fellow at Oxford University, in the Depatment of Biochemistry, England in 1978 and 1979, and a post doctorate fellow at Stanford University, California, USA in the Department of Biochemistry in 1998. He returned to the Biocenter in Basel in 1981. He was then research affiliate at the Theodor Kocher Institute in Bern and specialised in signal transduction, studying cellular responses related to cytokin binding. Since 1997 he has been Adj. Assistant Professor at the Human Performance Laboratory, the University of Calgary. His main field of research is the signal propagation controlling movement patterns of humans. This involves biophysical/biomedical measurements and the analysis of sensory systems.

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