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One of the most basic pieces of information gained from dynamic electromyography is accurately defining muscle action and phase timing within the gait cycle. The human gait relies on selective timing and the intensity of appropriate muscle activations for stability, loading, and progression over the supporting foot during stance, and further to advance the limb in the swing phase. A common clinical practice is utilizing a low-pass filter to denoise integrated electromyogram (EMG) signals and to determine onset and cessation events using a predefined threshold. However, the accuracy of the defining period of significant muscle activations via EMG varies with the temporal shift involved in filtering the signals; thus, the low-pass filtering method with a fixed order and cut-off frequency will introduce a time delay depending on the frequency of the signal. In order to precisely identify muscle activation and to determine the onset and cessation times of the muscles, we have explored here onset and cessation epochs with denoised EMG signals using different filter banks: the wavelet method, empirical mode decomposition (EMD) method, and ensemble empirical mode decomposition (EEMD) method. In this study, gastrocnemius muscle onset and cessation were determined in sixteen participants within two different age groups and under two different walking conditions. Low-pass filtering of integrated EMG (iEMG) signals resulted in premature onset (28% stance duration) in younger and delayed onset (38% stance duration) in older participants, showing the time-delay problem involved in this filtering method. Comparatively, the wavelet denoising approach detected onset for normal walking events most precisely, whereas the EEMD method showed the smallest onset deviation. In addition, EEMD denoised signals could further detect pre-activation onsets during a fast walking condition. A comprehensive comparison is discussed on denoising EMG signals using EMD, EEMD, and wavelet denoising in order to accurately define an onset of muscle under different walking conditions.
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One or two frequencies? The Iterative Filtering answers
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few years. However, even if its convergence and stability are now established both in the continuous and discrete setting, it is still an open problem to understand up to what extent this approach can separate two close-by frequencies contained in a signal. In this paper, first we recall previously discovered theoretical results about Iterative Filtering. Afterward, we prove a few new theorems regarding the ability of this method in separating two nearby frequencies both in the case of continuously and discrete sampled signals. Among them, we prove a theorem which allows to construct filters which captures, up to machine precision, a specific frequency. We run numerical tests to confirm our findings and to compare the performance of Iterative Filtering with the one of Empirical Mode Decomposition and Synchrosqueezing methods. All the results presented confirm the ability of the technique under investigation in addressing the fundamental “one or two frequencies” question.
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- Award ID(s):
- 2307465
- PAR ID:
- 10506887
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Applied Mathematics and Computation
- Volume:
- 462
- Issue:
- C
- ISSN:
- 0096-3003
- Page Range / eLocation ID:
- 128322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.amc.2023.128322
