Digital Butterworth filter for subtracting noise from low magnitude surface electromyogram

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Abstract

This work presents a digital filter designed to delimitate the frequency band of surface electromyograms (EMG) and remove the mains noise and its harmonics, focusing the signal analysis during reduced muscle activity. A Butterworth filter was designed as the frequency-domain product of a second order, high-pass filter with cutoff frequency 10 Hz, an eighth order low-pass filter, with cutoff at 400 Hz and six stop-band filters, second order, centered at the 60 Hz mains noise and its harmonics until 360 Hz. The resulting filter was applied in both direct and reverse directions of the signals to avoid phase distortions. The performance was evaluated with a simulated EMG signal with additive noise in multiples of 60 Hz. A qualitative assessment was made with real EMG data, acquired from 16 subjects, with age from 20 to 32 years. Subjects were positioned in orthostatic position during 21 s, being only the last second analyzed to assure stationarity. EMG were collected by Ag/AgCl electrodes on right lateral gastrocnemius, amplified with gain 5000, filtered in the band from 10 Hz to 1 kHz, and thus digitized with 2 ksamples/s. The filter effectively removed the mains noise components, with attenuations greater than 96.6%. The attenuation of the simulated signal at frequencies below 15 Hz and at 60 Hz caused only a small reduction of total power, preserving the original spectrum. Thus, the filter resulted suitable to the proposed application.

Introduction

The surface electromyography (SEMG) is a noninvasive technique for recording the electrical activity of the skeletal muscles, which is usually denominated EMG signal. This technique has many applications, such as the identification of the onset of muscular contraction, the muscular force estimation and the muscular fatigue monitoring [1], [2]. In such applications, particularly when the signal has low magnitude, the signal quality is usually affected by mains noise [3], [4].

Most of the studies with SEMG involve maximal or submaximal muscular contraction intensity, where the myoelectric activity is sufficient to present signal/noise ratio suitable for the acquisition of high quality signals. This does not happen however with the antigravitational muscles in quiet standing position, where the EMG signal presents very low magnitude which can seriously reduce the signal/noise ratio [5], in despite of using amplifiers with higher common mode rejection rate (CMMR > 100 dB). For such application, some data acquisition systems present specific filters for mains noise attenuation, as the analogical notch filter, which, in fact, attenuates a narrow frequency-band around the target frequency [6]. However, the undesirable frequency is not totally removed [4], and additional digital filtering is still necessary for an effective attenuation of mains noise. Additionally, if the acquired signal is saturated by the amplification, the mains noise will become a broadband noise with increased energy in higher harmonics, and the notch filter becomes inefficient and will occult the saturation, whatever the acquisition is being monitored in real-time. For that reasons, the analogical notch filters are becoming obsolete.

The purpose of this work is to describe and evaluate a band-pass Butterworth digital filter specifically designed for delimiting the band of interest of low magnitude EMG and to attenuate the 60 Hz mains noise and its harmonics, which overlap the signal.

Section snippets

Background

Several methods of filtering were proposed for movement artifact and electrical interference in EMG [7]. A low-pass analogical Butterworth filter, N order obeys the follow function in frequency domain (Fourier transform) [4], [8]:|H(jω)|2=11+(ω/ωC)2Nwhere |H(jω)|2 is the square magnitude of the frequency response of the filter, j=1, ω the angular frequency and ωC is the filter's cutoff frequency.

To project the analogical filter, the transfer function H(s) must be known, being expressed by a

Filter specifications and design

The filter was conceived to be employed to digital signals twice, in the direct and reverse order of samples to avoid phase drifts. It was obtained as the convolution of eight in series filters, comprehending a high-pass, a low-pass and six stop-band filters for the mains fundamental noise (60 Hz) and its first five harmonics.

For attenuation of movement artifacts and intrinsic instrumentation noise [7], it was designed a high-pass second order Butterworth digital filter with cutoff frequency 10 

Filter evaluation methods

To investigate the effects of the filter on low magnitude EMG signals corrupted by mains noise, the following approach was adopted. At first, a stationary EMG simulation was implemented in accordance with Stulen and De Luca [2] and 60 Hz noise and its harmonics were added to this signal. Furthermore, an experimental analysis of quiet stance was conducted to study the filter's attenuation on the real low magnitude signal.

The filter applications were performed with programs using the software

Simulated signal

The total power of the desired signal m was 28.07 (μV)2/s, and increased to 50.40 (μV)2/s with the addition of noise. The filter caused a decrease of the power to 26.22 (μV)2/s in mˆ. The small difference of power between m and mˆ is mainly explained by the attenuation in m at frequencies below 15 Hz and between 59 and 61 Hz, caused by the low-pass and the first stop-band filters, respectively, as shown in the superimposed power spectra of m and mˆ (Fig. 6). These attenuations do not affected MF,

Discussion

A digital filter was designed for pre-processing low magnitude EMG signals. The need of such filter was observed in previous work [5], focusing the myoelectric activity of the gastrocnemius muscle in quiet standing position. According to Caron [13], the force generated in such situation is about 10% of the maximal force of the muscle.

The project was presented with a second order high-pass filter and an eighth order low-pass filter with cutoff frequencies 10 and 400 Hz, respectively. These filter

Acknowledgements

This study was partially supported by the Brazilian Research Council (CNPq) and José Bonifácio University Foundation (FUJB). The first author wishes also to thanks the scholarships given by CAPES and FAPERJ Foundations.

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    Raw sEMG signals were sampled at 1000 Hz (differential amplifier, CMRR > 110 dB at 50 Hz, input impedance of 110 MΩ at 50 Hz). Raw sEMG signals were filtered for the reduction of power line interference using the technique described by Mello et al., (2007) modified for 50 Hz, and filtered with a 10 Hz high-pass and 450 Hz low-pass fourth-order Butterworth filters. Subsequently, the Root Mean Square (RMS) of the signal was computed using a 125 ms time-window length (Fig. 1).

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