Algorithm to demodulate an electromyogram signal modulated by essential tremor
© The Author(s) 2017
Received: 18 August 2016
Accepted: 13 May 2017
Published: 31 May 2017
Essential tremor is a disorder that causes involuntary oscillations in patients both while they are engaged in actions and when maintaining a posture. Such patients face serious difficulties in performing daily living activities such as meal movement. We have been developing an electromyogram (EMG)-controlled exoskeleton to suppress tremors to support the movements of these patients. The problem is that the EMG signal of the patients is modulated by the tremor signal as multiplicative noise. In this paper, we proposed a novel signal processing method to demodulate patients’ EMG signals. We modelled the multiplicative tremor signal with a powered sine wave and the tremor signal in the EMG signal was removed by dividing the modelled tremor signal into the EMG signal. To evaluate the effectiveness of the demodulation, we applied the method to a real patient’s EMG signal, extracted from biceps brachii while performing an elbow flexion. We quantified the effect of the demodulation by root mean square error between two kinds of muscle torques, an estimated torque from the EMG signal and calculated torque from inverse dynamics based on the motion data. The proposed method succeeded in reducing the error by approximately 15–45% compared with using a low-pass filter, typical processing for additive noise, and showed its effectiveness in the demodulation of the patients’ EMG signal.
KeywordsAssistive device Biosignal processing Electromyogram (EMG) signal Essential tremor Wearable robotics
Essential tremor is the most common pathological tremor, in which the tremor symptoms occur while the patient is performing an action or maintaining a posture. Researchers have indicated that older people often experience essential tremor. Some have reported that about 4% of the population above the age of 40 experience essential tremor , while others have reported it in 5–14% of individuals aged over 65 [2, 3]. Essential tremor can result in functional disability and causes social inconvenience. Approximately 65% of essential tremor patients have serious difficulties in performing daily activities such as meal movement [4, 5].
Current approaches for the suppression of essential tremor in practical use can be divided into two types: the use of medication to suppress the overreaction of the nerves, and the use of electrical stimulation to a specific part of the brain, which is called deep brain stimulation. However, both of these approaches have significant limitations, namely, the side effects of the medication, and the invasive nature of the implantation of electrodes into the brain, respectively. As a result, studies on alternative approaches are ongoing. Some researchers have used functional electrical stimulation to suppress the tremors [6–8]. Others have proposed various methods to suppress tremor mechanically. Yano et al. proposed an end-effector meal-assistant robot with an adaptive filter for tremor suppression [9, 10]. Komatsuzaki et al. proposed a tremor suppression method using a shock absorber .
Weight of the proposed exoskeleton
Specification and required specification of geared motor
No load speed (deg/s)
More than 80.0
Stall torque (Nm)
More than 1.0
The core of the proposed exoskeleton is the control of the motor. The motor is controlled by an electromyogram (EMG) signal from the patients. EMG signals are often used as input signals to control exoskeletons because an amplitude of EMG signals are almost relative to the level of muscle activation [18–24]. Based on the estimation of the voluntary muscle activation from the amplitude of EMG signal, the motor drives along with the estimated voluntary motion; that is, when the user intends to perform an action, the motor follows the intended action, and when the user intends to maintain a posture, the motor retains its posture and constrains the joint motion. The torque of the motor is transmitted to the biological arm via one of the frames of the exoskeleton. As a first evaluation, we have already reported that the amplitude of the oscillation was reduced by about 50–80% using the proposed exoskeleton controlled with a toggle switch . To reach the aforementioned final goal, as a next step, to control this exoskeleton along with the user’s intention, the accurate estimation of the voluntary movement from the EMG signal of the patients is the most important remaining technical challenge.
EMG signals of essential tremor patients
Some approaches to tremor signal removal have been proposed by previous researchers. Rocon et al. proposed an adaptive filter with a weighted-frequency Fourier linear combiner for the force and angular velocity data that they used for their proposed exoskeleton for tremor patients . Yano et al. developed an adaptive filter for force sensor data that was used in admittance control for a meal-assistance manipulator [9, 10]. This filter estimated the tremor frequency and attenuated the signal in the estimated frequency band using a band stop filter. Riviere et al. proposed a filtering algorithm for physiological tremors that arise during microsurgery . However, these studies aimed to reduce tremor noise in motion signals that were measured by sensors such as force sensors or position meters. In these signals, the effects of the tremors are observed as additive noise. Therefore, it is difficult to apply these methods to the patients’ EMG signal.
To remove multiplicative noise, the cepstral mean normalization  (CMN) and maximum a posteriori estimation CMN (MAP-CMN) methods are widely used in the field of speech recognition. However, CMN is not a real-time adaptive method, and MAP-CMN requires cepstral mean calculations based on a signal of sufficient length to provide superior performance. It is difficult to use such methods for controlling the exoskeleton, because the acceptable estimation delay for controlling the exoskeleton is shorter than that of speech recognition; the exoskeleton must follow the user’s motion as fluently as possible. Additionally, to design the removal filter for the multiplicative tremor signal during a motion, it is essential to adapt the filter for the characteristics of the tremor signal during the motion. However, there are almost no studies that focus on the characteristics of the multiplicative tremor noise during a particular motion except for our previous study [15, 16], because the main objectives of the related studies on the characteristics of the tremor signal in EMG were to use the signal information to diagnose the cause of tremor. Therefore, to control the exoskeleton accurately based on the EMGs of essential tremor patients during a meal movement, it is necessary to develop an approach that can treat a signal with multiplicative noise in real time and adapt it to the characteristics of the tremor signal during the movement.
Whether the proposed method successfully demodulates the real patient’s EMG signal.
Whether the proposed method works well for both signals extracted while performing an action and while maintaining a posture, because essential tremor is a postural and an action tremor, and the characteristics of the signal vary based on the movement state.
In this section, we describe the detail about the proposed demodulation algorithm and describe how to evaluate the effect of the proposed method.
Concept of the proposed method
Model of the tremor signal
The model needs to represent the periodic characteristic of the tremor signals, in which the amplitude rises and falls alternately.
The modulation strength N D must be greater than zero because when the modulation strength N D is zero, the filtered signal s n goes to infinity in Eq. (1).
When the EMG signal of the essential tremor patients are not modulated, the modulation strength N D needs to equal one because the filtered signal equals the measured EMG signal.
Compared with previous work by Bacher et al. , we added a sigmoid function f(C MAX ) as a threshold function to implement the proposed algorithm only when the EMG signal is modulated by tremor. Further, we used a powered sine wave instead of a sine wave because a powered sine wave worked well for demodulation by trial and error.
To use the model for real-time demodulation, we needed to define some of parameters in (2). How to calculate the parameters is described in the following subsections.
Phase detection of powered sine wave
The tremor frequency F is one parameter that must be defined to demodulate the EMG signal. The tremor frequency of an individual patient varies, depending on the movement state of the patient (i.e., whether the patient is performing a voluntary movement or maintaining a posture) [15, 16]; however, the range of the variation is small. Therefore, the tremor frequency was set at 5 Hz, which is the main tremor frequency of the patient in the experiment. This parameter needs to be set individually.
Order of the powered sine wave
The order of the powered sine wave k is another parameter of the estimated tremor signal. We tested several values for the preliminary value of the order and found that a squared sine wave was the best wave for the demodulation process, and that the effect of changing the order was small. Therefore, we used the squared sine wave.
Processed with an LPF only (cutoff = 10 Hz).
Processed with an LPF (cutoff = 10 Hz) and the demodulation filter with constant parameters.
Processed with an LPF (cutoff = 10 Hz) and the demodulation filter with the proposed parameter setting.
Parameter values of the previous and the proposed methods
Modulation depth (a.u.)
Order of the powered sin wave (a.u.)
The participant in this experiment was an essential tremor patient (male, 70 years old) who had tremor symptoms, particularly in forearm rotation and in elbow flexion/extension. The tremor signals in the EMG signal were measured from the biceps brachii and the main signal frequency was approximately 5 Hz. We gave the participant a detailed account of our experimental objectives, made it clear that he was entitled to stop the experiment whenever he desired, and obtained his consent. This experiment was approved by the Institutional Review Board of Waseda University (Approval Number: 2012-196).
Body weight of the patient and weight of the inertial load
Body weight of the patient (kg)
Weight of bottle (kg)
0.017 (empty bottle)
0.337 (half full bottle)
0.575 (full bottle)
Muscle torque estimated from EMG signal
Muscle torque calculated by inverse dynamics
Physical properties of forearm and hand
Proportion of COG of forearm
Mass ratio of forearm
Radius of gyration of forearm
Proportion of COG of hand
Mass ratio of hand
Radius of gyration of hand
Length of parts of the patient body
Length of forearm (m)
Length of a hand (m)
According to research that estimates the muscle torque from the EMG signal and estimates the joint angle by solving dynamics problems , the coefficient of viscosity was set at 0.2.
Reduction rate of the RMSE
Condition of bottle
States of movement
Performing a flexion
Maintaining a posture
Effect of demodulation
In this experiment, using the proposed method, condition (3), the RMSE between the estimated data and the ground truth data was statistically significantly decreased in all cases. Compared with the results of the control condition, condition (2), by adjusting the modulation depth M, the proposed method succeeded in reducing errors when the patient performed an elbow flexion in all cases. From these results, our proposed demodulation algorithm was effective for the modulated EMG signal, and the adjustment worked well for the characteristic change of the tremor signal between the postural state and the flexion.
The reason that the reduction rate varied depending on both the state of movement and the weight of the bottle is likely the influence of the voluntary signal. The voluntary signal modulates the tremor signal. As described in Section I, the tremor signal is noise in the voluntary movement signal. Conversely, the voluntary signal is also noise in the tremor signal; that is, the tremor signal is modulated strongly if patients contract their muscles strongly. This modulation made it difficult to demodulate the EMG signal, because the tremor signal could not be simulated accurately when it was modulated. Therefore, to promote the proposed demodulation algorithm, we need to analyse the characteristic change in the tremor signal depending on the voluntary signal in some way, such as a time–frequency analysis or the change in the shape of the EMG signal, and then revise the processing method.
Number of participants
Patient-dependent parameters, such as frequency of tremor signal, are measured before the use of the proposed algorithm.
Patients with essential tremor who have their tremor source in their biceps brachii perform actions with elbow flexion such as drinking and eating.
In the first condition, although the EMG is noisy and varies across individuals, the major characteristics of the tremor signal, “grouped discharge”, is typical for the patients, and the proposed method can work for the tremor signal if patient-dependent parameters are fitted to each patient. However, in the second condition, the evaluation did not guarantee the effectiveness of the proposed method in all the conditions because the affected muscle is patient-dependent. The proposed method only showed its effectiveness for the EMG signal from biceps brachii while performing an elbow flexion. Therefore, although the guaranteed effect from this experiment was limited, as far as the target movement of the exoskeleton, this method can be applied for demodulating the EMG signal of the patients.
Effects on the control of the exoskeleton
From these discussions, the effects of the proposed demodulation algorithm have been validated. However, we have not discussed whether the effects are sufficient for controlling the exoskeleton. To address this, we have to use the proposed method on the exoskeleton and evaluate the controlled performances of the exoskeleton while a participant is wearing it. The RMSE between the muscle torque estimated from the EMG signal and the muscle torque calculated by solving the inverse dynamics problem directs the controlled performance, because the movement of the exoskeleton is defined based on Eq. (13). We hope that the proposed method promotes the controlled performance of the exoskeleton. In future work, we will evaluate the proposed demodulation algorithm using the exoskeleton to discuss whether the effects are sufficient.
The objectives of this paper were to develop an algorithm to demodulate the EMG signal of essential tremor patients whose EMGs combine information about both the voluntary movement and the tremor. The EMGs of the patients is modulated by the tremor signal as multiplicative noise. Therefore, to control the exoskeleton accurately, it is essential to demodulate the EMG signal. The proposed algorithm simulates the tremor signal by approximating the tremor signal with a powered sine wave, and then divides the approximated tremor signal into the EMG signals of the patients. To simulate the tremor signal accurately, parameters of the approximation were set based on the characteristic of the real patient’s EMG. Especially, we set the modulation depth, represent the gain of the modulation by tremor, as a variable to treat the characteristic change depending on the movement state. To evaluate the effect of the proposed method, we compared the RMSE between the muscle torque estimated from the EMG signal of the patient and the muscle torque calculated by solving the inverse dynamics problem, in three situations: without using the demodulation algorithm, using the demodulation algorithm (constant parameters), and using the proposed demodulation algorithm (modulation depth was variable). From this evaluation, we confirmed that our proposed method has a large effect on demodulating the modulated EMG signal regardless of the patient’s movement state. As far as its application to the exoskeleton, the method can be applied on the EMGs of patients. However, the effect varies depending on the strength of the voluntary movement.
In future work, to improve our algorithm, we need to analyse the characteristic changes in the tremor signal depending on the strength of the voluntary signal in some way, such as time–frequency analysis or by evaluating EMG signal shape changes, and then revise the processing method. Following this, we will implement our proposed algorithm in the controller of the exoskeleton and evaluate whether the proposed algorithm is sufficient for controlling the exoskeleton.
YM devised the basic concept of the overall system, technically developed the algorithm, carried out the experiments, analysed the data, and drafted the manuscript. MS devised the basic concept of the overall system, technically developed the algorithm, and carried out the experiments. YS, TA, and YK devised the research plan, and carried out the experiments. HI and MN drew the research design based on the clinical point of view. MF devised the basic concept and drew the research design of the overall study. All authors read and approved the final manuscript.
The authors sincerely thank the patient volunteer for participating in our experiment. This work was supported by the Japan Society for the Promotion of Science under a Grant-in-Aid for Scientific Research (S) (No. 25220005), a Grant-in-Aid for Challenging Exploratory Research (No. 15K12606), and a Grant-in-Aid for JSPS fellows (No. 13J05428); and by Fukushima Prefecture under the Fukushima Project on the Development of Medical and Welfare Devices, Fukushima, Japan.
The authors declare that they have no competing interests.
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