The EMG signal provides useful information about the muscle force developed under volitional muscle contraction. In the time domain, the rectified EMG envelope has been widely used for various applications, ranging from simple On/Off activation trigger  to muscle force estimation (e.g. [1, 26, 27]).
In cases of hybrid activation, i.e., when ES is being used to augment volitional muscle activation, the rectified EMG can be used either as a control signal [4–6, 14, 16], or as a muscle force estimator . In this mode of activation the volitional and ES-induced components of the EMG mix up together, and extraction of the volitional component from the raw EMG signal is required for monitoring and control purposes, necessitating multi-step processing procedures. Methods to extract the volitional component out of the raw EMG signal during hybrid activation have been developed (e.g., [6, 12, 16]). Few of these reports validate the success in extracting the volitional EMG. To accomplish that, the hybrid EMG signal was emulated by adding up together its volitional and induced components [7, 16].
In these latter studies muscle was under static contraction and the EMG signals were represented mathematically (i.e., by an explicit mathematical equation); thus the extraction process necessitated complex processing procedures such as filtration with adaptive filters , or Gram-Schmidt prediction error filters .
Several methods were used for evaluation of the success of extraction of the volitional EMG. The basic one was by visual inspection of the approximated signal which, despite not providing information on the processing method accuracy, can tell if the signal can be successfully utilized for control purposes [4–6, 9, 14].
More advanced methods utilized mathematical parameters to score the processing success. Yoem et al.  used three evaluation criteria: (a) visual inspection of the power spectra of the signals; (b) comparison of the signals' RMS values; and (c) 'false-positive' parameter that calculated the number of times in which the extracted signal peak amplitude is higher than the maximum value of the pure original EMG ingredient. The obtained parameters' values, which indicated: good visual matching, RMS value close to 1, and small 'false-positive' value, enabled the authors to conclude that a 6th order Gram-Schmidt prediction error filter successfully preserves the original volitional EMG signal.
Sennels et al.  illustrated various quantitative tools to test several configurations of adaptive filters. They showed, that for simulated data the adaptive filters they used were relatively insensitive to variations in the muscle responses; however for real-data, it was better to use adaptive filter with a large number of elements. Their results led them to the conclusion that a 6-element adaptive filer can successfully eliminate the ES share from the hybrid EMG signal.
The methodology developed in the present study was different in two respects: (a) each of the activation components was the result of dynamic, rather than static contraction, and (b) the signals were represented numerically, by means of their sampled actual values, obtained from repetitive dynamic contraction data simulating typical gait-like activity of the TA muscle during a swing phase. The advantage of this approach is that it better reflects real-life situation, whereby signals are normally dynamic, rather than static and they may not always be represented mathematically.
Additionally, since we were interested in the EMG envelope of the volitional component rather than in its raw signal, the resulting processing scheme turned to be much simpler than the one developed in the abovementioned previous works. This concept is different from other works, in which it is first attempted to obtain the raw volitional signal, and then apply standard processing routines to derive its envelope [4–6, 8, 12, 16, 20]. The idea here is that since the envelope pattern is smoother and well-defined compared to the raw EMG, it can be recovered more accurately and with less complexity, compared to the traditional methods. Those advantages are of great relevance when using the procedure for real-time applications.
Basically, the signal processing scheme relies on commonly used routines, involving 'rigid' and 'flexible' modules. The 'rigid' modules, which include high-pass filtration, signal rectification, and low-pass filtration, are commonly used for EMG envelope calculations (e.g.: [1, 20]); and the 'flexible' modules are commonly found in the context of ES artifacts removal [6, 12, 15, 17, 21]. The role of each module in the process is well defined: The "Artifact Blocking Window" module suppresses the ES artifact (e.g.: [6, 12], ). The Comb-filter filtration module further cleans the signal from the ES component . The Rectified signal peak envelope module provides a rough representation of the EMG envelope, and reconstructs its pattern in regions where the signal has been chopped out for artifact suppression (e.g., in the blocked regions). A processing scheme that combines together these modules is not found in literature.
Several works dealt with the ES artifact with utilization of only one of the above modules; mostly Comb-filter filtration or Artifact Blocking Window [12, 20, 21]. Frigo et al.  have used both Comb-filter filtration and Artifact Blocking Window modules, and reported on improved elimination of ES component.
Our work has shown that all three 'flexible' modules are necessary for the appropriate elimination of the ES component from the overall signal. However, when only the Comb-filter or Artifact Blocking Window module takes part in the process, we demonstrated that inclusion of the Rectified peak envelope module was not necessary and could introduce substantial errors. This is because the Rectified Peak Envelope module is only effective when the signal is completely cleaned from its ES component.
When the Comb-filter filtration and Artifact Blocking Window were joined together in the process, the rectified signal did not have any substantial ES remainders and the envelope reconstruction was successful. However, when only one of the above modules was used, there were still some ES residuals  that led to an erroneous envelope reconstruction.
It should be noted, though, that in the Rectified signal peak envelope module, a complete period of the signal is required in order to reconstruct its blocked regions. This introduces a time delay of one period, thus preventing real-time application of the Rectified signal peaks envelope module. For real-time applications, the literature has suggested several solutions to emulate the operation of this module, the most common being a blocking window with an average signal value, or a holder that retains the pre-blocking last sample value of the signal [8, 20, 21]. This allows for the reconstruction of the missing samples, thus providing its real-time envelope approximation.
To compare between the calculated volitional EMG-envelope (i.e., from synthetic database) and the actual one (from volitional only tests), we used two parameters, RMSE and MAE, for the large and small scale comparisons, respectively.
The RMSE expresses the mean difference between two signals, and reflects their general similarity. This parameter is widely used in literature (e.g: [7, 22]).
The MAE parameter expresses the difference between the approximated and actual signal amplitudes. Assuming that the signals do not have any difference in phase and shape, the difference in amplitudes represents the local error. Since many applications use the value of the EMG envelope as a control signal [4–6, 8, 12], MAE becomes important and knowledge of the envelope approximation error is required for system design. A similar MAE analysis is not found in literature, probably since all the related works dealt with recovery of the raw volitional-EMG signal and not of its envelope (e.g., [7, 20, 21, 23]).
The suggested method in our work provides rational evaluators for the performance of the various schemas. These, however, are not the only possible evaluators. For instance, Sennels et al  used other evaluators to test the success of their methods. The first evaluator was used on simulated data, and examined the ratio between the input signal to noise ratio (SNR) and the output SNR; the second evaluator was used on real-data, and examined the power reduction of the input and output signals. Thus, further works should enable unbiased comparisons between current and earlier works.
It is noticeable that the variance of the MAE, and RMSE values between the subjects was high. Several reasons can lead to such behavior; e.g.: differences in anatomy, tissue structure, muscle fatigue, etc., which have an effect on the subject's ES pattern, and therefore on the schema performance. Nevertheless, for the selected schema, the obtained low values of RMSE and MAE (RMSE: 1.21 – 3.85%, MAE: 7.58 – 10.46%) in all the subjects but one, indicate the high accuracy of the processing method, and point out that the preferred computational scheme should include all modules.
A major assumption was made in this work, according to which the hybrid EMG can be represented by the superposition of the volitional only and induced only EMG signals. This assumption relied on a preliminary work, which verified that a superimposed signal has the characteristics of an actual hybrid signal; thus, the superimposed hybrid signal has a typical spike and M-wave which can be related to the ES component, together with a stochastic-like signal resulting from the volitional component. In addition, since the origins of the superimposed signal are known, we can establish an unbiased comparison between the various signal-processing schemes and their ability to satisfactorily resolve the hybrid signal into its components.
When a preferred signal-processing scheme is obtained, we can apply it to an in-vivo hybrid EMG signal with high certainty that the process outcome well-describes the hybrid signal origins.
Another assumption was that the simulated dynamic motion torque reflects the actual gait profile. This assumption should be further examined due to the fact that the actual gait motion is non-isometric, and is influenced by body kinematics that could in turn be reflected on the volitional and induced EMG signals. Nevertheless, the generality of the selected schema enables its implementation to more realistic gait-like signals without any noticeable changes.