Blind separation of linear instantaneous mixtures of nonstationary surface myoelectric signals

Electromyographic (EMG) recordings detected over the skin may be mixtures of signals generated by different active muscles due to the phenomena related to volume conduction. Separation of the sources is necessary when single muscle activity has to be detected. Signals generated by different muscles may be considered uncorrelated but in general overlap in time and frequency. Under certain assumptions, mixtures of surface EMG signals can be considered as linear instantaneous but no a priori information about the mixing matrix is available when different muscles are active. In this study, we applied blind source separation (BSS) methods to separate the signals generated by two active muscles during a force-varying task. As the signals are non stationary, an algorithm based on spatial time-frequency distributions was applied on simulated and experimental EMG signals. The experimental signals were collected from the flexor carpi radialis and the pronator teres muscles which could be activated selectively for wrist flexion and rotation, respectively. From the simulations, correlation coefficients between the reference and reconstructed sources were higher than 0.85 for signals largely overlapping both in time and frequency and for signal-to-noise ratios as low as 5 dB. The Choi-Williams and Bessel kernels, in this case, performed better than the Wigner-Ville one. Moreover, the selection of time-frequency points for the procedure of joint diagonalization used in the BSS algorithm significantly influenced the results. For the experimental signals, the interference of the other source in each reconstructed source was significantly attenuated by the application of the BSS method. The ratio between root-mean-square values of the signals from the two sources detected over one of the muscles increased from (mean +/- standard deviation) 2.33 +/- 1.04 to 4.51 +/- 1.37 and from 1.55 +/- 0.46 to 2.72 +/- 0.65 for wrist flexion and rotation, respectively. This increment was statistically significant. It was concluded that the BSS approach applied is promising for the separation of surface EMG signals, with applications ranging from muscle assessment to detection of muscle activation intervals, and to the control of myoelectric prostheses.     

Modeling of surface myoelectric signals. I. Model implementation

The relationships between the parameters of active motor units (MU's) and the features of surface electromyography (EMG) signals have been investigated using a mathematical model that represents the surface EMG as a summation of contributions from the single muscle fibers. Each MU has parallel fibers uniformly scattered within a cylindrical volume of specified radius embedded in an anisotropic medium. Two action potentials, each modeled as a current tripole, are generated at the neuromuscular junction, propagate in opposite directions and extinguish at the fiber-tendon endings. The neuromuscular junctions and fiber-tendon endings are uniformly scattered within regions of specified width. Muscle fiber conduction velocity and average fiber length to the right and left of the center of the innervation zone are also specified. The signal produced by MU's with different geometries and conduction velocities are superimposed. Monopolar, single differential and double differential signals are computed from electrodes placed in equally spaced locations on the surface of the muscle and are displayed as functions of any of the model's parameters. Spectral and amplitude variables and conduction velocity are estimated from the surface signals and displayed as functions of any of the model's parameters. The influence of fiber-end effects, electrode misalignment, tissue anisotropy, MU's location and geometry are discussed. Part II of this paper will focus on the simulation and interpretation of experimental signals.     

一种基于奇异值分解的改进信噪比盲估计算法

针对空间分解类信噪比(SNR)估计算法中子空间维数估计复杂度较高,低信噪比下估计偏差较大的问题,提出了一种改进的子空间维数估计算法。该算法首先利用样本自相关矩阵的奇异值序列进行后向差分得到梯度序列,对梯度序列每一项与后5项之和的比值进行搜索,最大比值所对应的奇异值序号作为信号子空间维数,最后计算信噪比。合适数据长度下的仿真结果表明：在信噪比-5 dB~20 dB范围内,常规通信信号的信噪比估计平均偏差小于0.5 dB,标准差小于1 dB;该算法提升了低信噪比下的估计性能,运算量较小,无需知道调制方式、载波频率、符号率等先验信息,在低信噪比时对信噪比时变的跟踪估计更为准确,且对复杂高阶调制信号同样适用。     

Fatigue compensation of the electromyographic signal for prostheticcontrol and force estimation

During a sustained muscle contraction, the amplitude of electromyographic (EMG) signals increases and the spectrum of the EMG signal shifts toward lower frequencies. These effects are due to muscular fatigue and can cause problems in the control of myoelectric prostheses and in the estimation of contraction level from the EMG signal. It has been well known that the fatigue effects can be explained by the conduction velocity changes during the fatigue process and by the idea that the conduction velocity is linearly proportional to the median frequency of EMG signals. Hence the fatigue process can be monitored by measuring the median frequency. A fatigue compensation preprocessor has been developed. It uses the widely accepted power spectrum density model of EMG signals that contains the conduction velocity as a measure of fatigue. It was verified that the preprocessor scales down the amplitude of the fatigued EMG signal and decompresses the spectrum. Hence, the preprocessor eliminates the increase in amplitude and the shift in frequency and enables consistent EMG signals to be used to control prostheses     

采用基于互补序列分组编码的OFDM系统性能分析与仿真

为了减小正交频分复用（OFDM）信号的峰值-平均值功率之比（PAPR），本文利用互补序列和Reed-Muller码的关系，详细提出了一种构造互补序列的分组编码方法的具体实现方案。分析了其在AWGN和选频衰落信道中的性能，并做了相应的仿真。仿真结果表明，编码后每个OFDM信号的最大PAPR不超过3dB；采用该编码方法的OFDM在AWGN中当信噪比不到11dB时就可以实现BER为10^-6，在衰落信道中如果采用软判决译码，则当信噪比达到20dB左右时可以实现BER为10^-3。     

Motor unit conduction velocity distribution estimation from evoked motor responses

Action potentials travel along the muscle fibers with a specific conduction velocity that depends on their structural and functional properties. Only the estimation of muscle conduction velocity distribution (MCVD) may be able to depict this propagation heterogeneity. Based on the method proposed by Cummins et al. (Electroenceph Clin Neurophysiol, 46:647-658, 1979) to estimate nerve conduction velocity distribution (NCVD), the present paper proposes a method that modifies the Cummins' approach to make it suitable for MCVD estimation from electrically evoked motor responses. The MCVD estimation algorithm was first assessed by means of simulated signals in order to control all signal features during the optimization process. Simulations showed that estimated distributions were very close to the true ones when taking into account the specificities of the muscle action potential, due to its generation and extinction (MSE divided by 5 on distribution standard deviation). This method was then applied to real signals. Elicited motor responses were recorded on the biceps brachii of healthy subjects either during repeated maximal stimulations at 20 Hz or during increasing intensity stimulations at 1 Hz. MCVD estimates were used to analyze fatigue and motor unit recruitment processes, respectively.     

Modeling of surface myoelectric signals. II. Model-based signalinterpretation

Experimental electromyogram (EMG) data from the human biceps brachii were simulated using the model described in [10] of this work. A multichannel linear electrode array, spanning the length of the biceps, was used to detect monopolar and bipolar signals, from which double differential signals were computed, during either voluntary or electrically elicited isometric contractions. For relatively low-level voluntary contractions (10%-30% of maximum force) individual firings of three to four-different motor units were identified and their waveforms were closely approximated by the model. Motor unit parameters such as depth, size, fiber orientation and length, location of innervation and tendonous zones, propagation velocity, and source width were estimated using the model. Two applications of the model are described. The first analyzes the effects of electrode rotation with respect to the muscle fiber direction and shows the possibility of conduction velocity (CV) over- and under-estimation. The second focuses on the myoelectric manifestations of fatigue during a sustained electrically elicited contraction and the interrelationship between muscle fiber CV, spectral and amplitude variables, and the length of the depolarization zone. It is concluded that a) surface EMG detection using an electrode array, when combined with a model of signal propagation, provides a useful method for understanding the physiological and anatomical determinants of EMG waveform characteristics and b) the model provides a way for the interpretation of fatigue plots.     

A robust parametric estimator for single-trial movement relatedbrain potentials

Current estimators for single-trial evoked potentials (EP's) require a signal-to-noise ratio (SNR) of 0 dB or better to obtain high quality estimations, yet many types of EP's suffer from substantially lower SNR's. This paper presents a robust-evoked-potential-estimator (REPE) facilitating high quality estimations of single movement related EP's with a relatively low SNR. The estimator is based on a standard ARX model, enhanced to support estimation under poor SNR conditions. The REPE was tested successfully on a computer simulated data set giving reliable single-trial estimations for the low SNR range of around -20 dB. The REPE was also applied to experimental data, producing clear single-trial estimations of movement related brain signals recorded in a classic scenario of self-paced finger tapping experiment     

Nerve-bundle conduction velocity distribution measurement and transfer function analysis

Human peripheral nerves are composed of thousands of individual nerve fibers whose signal conduction velocities vary from 0.2 to 100 m/s. Though good correlation exist between fiber velocity and the physiological function subserved by these fibers, considerable variation is found for specific end organs (20 to 40 m/s for a single muscle). Though clinical neurophysiologists have routinely measured the maximum conduction velocity of peripheral motor nerves for 30 years, it has not been possible to determine the velocity distributions. This report details a model and noninvasive methodology for motor axon conduction latency distribution mesurement. This distribution, proportional to velocity dispersion, possesses a low-pass filter characteristic which agrees with theoretical predictions and may be significant in some sensory and motor functions.     

A fast and reliable technique for muscle activity detection from surface EMG signals

The estimation of on-off timing of human skeletal muscles during movement is an important issue in surface electromyography (EMG) signal processing with relevant clinical applications. In this paper, a novel approach to address this issue is proposed. The method is based on the identification of single motor unit action potentials from the surface EMG signal with the use of the continuous wavelet transform. A manifestation variable is computed as the maximum of the outputs of a bank of matched filters at different scales. A threshold is applied to the manifestation variable to detect EMG activity. A model, based on the physical structure of the muscle, is used to test the proposed technique on synthetic signals with known features. The resultant bias of the onset estimate is lower than 40 ms and the standard deviation lower than 30 ms in case of additive colored Gaussian noise with signal-to-noise ratio as low as 2 dB. Comparison with previously developed methods was performed, and representative applications to experimental signals are presented. The method is designed for a complete real-time implementation and, thus, may be applied in clinical routine activity.     

An analysis of signal-to-noise ratio and design parameters of aterahertz optical asymmetric demultiplexer

Analysis of the signal-to-noise ratio (SNR) as a function of the component parameters in a terahertz optical asymmetric demultiplexer (TOAD) can help optimize its performance as a demultiplexer or as a router in an optical time division multiplexed network. The analysis presented here accounts for crosstalk due to deviation from a perfect 3 dB splitting ratio in the TOAD's 2×2 coupler, and the degradation of SNR due to fluctuations in the control pulse energy. The spontaneous emission noise output of the semiconductor optical amplifier (SOA) contained in the TOAD is simulated under different degrees of saturation. The analysis indicates that leakage due to the asymmetric placement of the SOA contributes significantly to the crosstalk. To achieve a SNR of 21.5 dB or higher in a 100 Gb/s system, one must use a 2×2 coupler that deviates less than 1% from a perfect 3 dB splitting ratio. Also, control pulse energy fluctuations must be less than 10% for a 20-GHz bandwidth electronic receiver. Novel crosstalk-free designs are proposed and analyzed which meet the stringent requirements of current TOAD devices. A significant enhancement in SNR is predicted when the SOA is operated near the optimal saturation point     

The spatial integration effect of surface electrode detectingmyoelectric signal

The spectral properties of surface electrodes used for myoelectric signal detection were investigated using both a theoretical and an experimental approach. On the basis of the theoretical model, the single surface electrode was found to act as a low pass filter depending on the electrode diameter (d) and the fiber conduction velocities (CV). Several dips in the power spectrum were also predicted for varying frequencies depending on d and CV. The mathematical expression of the surface electrode filter was highly consistent with previously demonstrated properties of the single fiber power spectrum. An experimental comparison between myoelectric signals from the vastus lateralis muscle recorded using two electrode pairs with different diameters confirmed this low pass filter effect. However, the dip phenomenon was not observed from experimental data. The practical consequences of the electrode filter effect are discussed with respect to the interpretation of changes in surface myoelectric signal spectrum, particularly when a shift toward the high frequencies is observed.     

Estimation of motor unit conduction velocity from surface EMG recordings by signal-based selection of the spatial filters

Muscle fiber conduction velocity (CV) can be estimated by the application of a pair of spatial filters to surface electromagnetic (EMG) signals and compensation of the spatial filter transfer function with equivalent temporal filters. This method integrates the selection of the spatial filters for signal detection to the estimation of CV. Using this approach, in this paper, we propose a novel technique for signal-based selection of the spatial filter pair that minimizes the effect of nonpropagating signal components (end-of-fiber effects) on CV estimates (optimal filters). The technique is applicable to signals with one propagating and one nonpropagating component, such as single motor unit action potentials. It is shown that the determination of the optimal filters also allows the identification of the propagating and nonpropagating signal components. The new method was applied to simulated and experimental EMG signals. Simulated signals were generated by a cylindrical, layered volume conductor model. Experimental signals were recorded from the abductor pollicis brevis with a linear array of 16 electrodes. In the simulations, the proposed approach provided CV estimates with lower bias due to nonpropagating signal components than previously proposed methods based on the entire signal waveform. In the experimental signals, the technique separated propagating and nonpropagating signal components with an average reconstruction error of 2.9 +/- 0.9% of the signal energy. The technique may find application in single motor unit studies for decreasing the variability and bias of CV estimates due to the presence and different weights of the nonpropagating components.     

Switched-diversity FSK in frequency-selective Rayleigh fading

This paper presents the measured performance of a 64 kbit/s switched-diversity FSK receiver subjected to simulated frequency-selective Rayleigh fading. The single receiver input is switched between two, three, or four uncorrelated Rayleigh-fading signals whenever the instantaneous receiver output falls below a threshold. The optimum level of this threshold relative to the mean signal level is relatively insensitive to frequency selectivity and vehicle speed. A nearly optimum threshold may be determined using an AGC amplifier and fixed comparator. Switched diversity is a powerful tool for combating frequency selectivity and Rayleigh fading. Two-branch switched diversity can achieve 10^-2BER, with 6 dB lower SNR than that needed without diversity. In the absence of frequency selectivity, two-branch switched diversity can perform within 3 dB SNR of maximal-ratio diversity and within 1 dB of selection diversity. Switched diversity can achieve BER's lower than the irreducible single-channel BER produced by frequency selectivity. Four-branch switched diversity typically requires 4 dB lower SNR to achieve a given BER than does two-branch switched diversity.     

Switched-Diversity FSK in Frequency-Selective Rayleigh Fading

This paper presents the measured performance of a 64 kbit/s switched-diversity FSK receiver subjected to simulated frequency-selective Rayleigh fading. The single receiver input is switched between two, three, or four uncorrelated Rayleigh-fading signals whenever the instantaneous receiver output falls below a threshold. The optimum level of this threshold relative to the mean signal level is relatively insensitive to frequency selectivity and vehicle speed. A nearly optimum threshold may be determined using an AGC amplifier and fixed comparator. Switched diversity is a powerful tool for combating frequency selectivity and Rayleigh fading. Two-branch switched diversity can achieve 10^-2BER, with 6 dB lower SNR than that needed without diversity. In the absence of frequency selectivity, two-branch switched diversity can perform within 3 dB SNR of maximal-ratio diversity and within 1 dB of selection diversity. Switched diversity can achieve BER's lower than the irreducible single-channel BER produced by frequency selectivity. Four-branch switched diversity typically requires 4 dB lower SNR to achieve a given BER than does two-branch switched diversity.     

Multiple site electromyograph amplitude estimation

Temporal whitening of individual surface electromyograph (EMG) waveforms and spatial combination of multiple recording sites have separately been demonstrated to improve the performance of EMG amplitude estimation. This investigation combined these two techniques by first whitening, then combining the data from multiple EMG recording sites to form an EMG amplitude estimate. A phenomenological mathematical model of multiple sites of the surface EMG waveform, with analytic solution for an optimal amplitude estimate, is presented. Experimental surface EMG waveforms were then sampled from multiple sites during nonfatiguing, constant-force, isometric contractions of the biceps or triceps muscles, over the range of 10-75% maximum voluntary contraction. A signal-to-noise ratio (SNR) was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Results showed that SNR performance: 1) increased with the number of EMG sites, 2) was a function of the sampling frequency, 3) was predominantly invariant to various methods of determining spatial uncorrelation filters, 4) was not sensitive to the intersite correlations of the electrode configuration investigated, and 5) was best at lower levels of contraction. A moving average root mean square estimator (245-ms window) provided an average ± standard deviation (A±SD) SNR of 10.7±3.3 for single site unwhitened recordings. Temporal whitening and four combined sites improved the A±SD SNR to 24.6±10.4. On one subject, eight whitened combined sites were achieved, providing an A±SD SNR of 35.0±13.4     

Influence of tissue inhomogeneities on noninvasive muscle fiberconduction velocity measurements-investigated by physical and numericalmodeling

The determination of conduction velocity in the muscle fibers of single motor units from noninvasive recordings of single motor unit action potentials can be improved by the method of spatially filtering multielectrode EMG. The use of this conduction velocity as a diagnostic tool requires a high reliability of the detected values. However, experiments did reveal that the measured conduction velocity values showed remarkably high fluctuations depending on the recording site along the muscle fibers which could not be attributed to the influence of the endplate and tendon region. The present work examines the hypothesis that the observed fluctuations in propagation velocity were caused by electrically inhomogeneous tissue, regions of different electrical conductivity which are located between the excited muscle fibers and the recording electrodes and which cause a deformation of the extracellular electric current field. The investigation was performed by means of a physical model as well as by finite element model calculations. In both models single, simple shaped (cylindrical) inhomogeneity regions with a conductivity of 0.1 to 10 times that of the surrounding medium and diameters ranging between 1.6 and 2.7 mm were placed between excitation sources and recording site. The results indicate that the observed conduction velocity fluctuations of up to some 10% can be well attributed to inhomogeneity effects of the tissue conductivity. Based on these results, one may look for signal processing methods to cut down such fluctuations in conduction velocity measurements.     

Assessment of average muscle fiber conduction velocity from surface EMG signals during fatiguing dynamic contractions

In this paper, we propose techniques of surface electromyographic (EMG) signal detection and processing for the assessment of muscle fiber conduction velocity (CV) during dynamic contractions involving fast movements. The main objectives of the study are: 1) to present multielectrode EMG detection systems specifically designed for dynamic conditions (in particular, for CV estimation); 2) to propose a novel multichannel CV estimation method for application to short EMG signal bursts; and 3) to validate on experimental signals different choices of the processing parameters. Linear adhesive arrays of electrodes are presented for multichannel surface EMG detection during movement. A new multichannel CV estimation algorithm is proposed. The algorithm provides maximum likelihood estimation of CV from a set of surface EMG signals with a window limiting the time interval in which the mean square error (mse) between aligned signals is minimized. The minimization of the windowed mse function is performed in the frequency domain, without limitation in time resolution and with an iterative computationally efficient procedure. The method proposed is applied to signals detected from the vastus laterialis and vastus medialis muscles during cycling at 60 cycles/min. Ten subjects were investigated during a 4-min cycling task. The method provided reliable assessment of muscle fatigue for these subjects during dynamic contractions.     

一种平坦衰落信道下的盲信噪比估计算法

针对基于子空间分解信噪比估计算法中信号子空间维数估计复杂度高、小样本条件下估计偏差大的问题,提出了一种改进的盲信噪比估计算法.该算法首先构造接收信号的自相关矩阵,然后从矩阵奇异值序列的尾部开始,间隔两项依次进行差分得到梯度序列,再以梯度序列相邻两项均值大干特定阈值为条件确定信号子空间的维数,最后求得信噪比.仿真结果表明:信噪比范围为-5～+15 dB时,平坦衰落信道下常用调制信号的信噪比估计标准差小于0.1 dB,与MDL,AIC方法相比,该算法计算量小,且能适应更低的信噪比和更短的数据长度.     

Physiologically based simulation of clinical EMG signals

An algorithm that generates electromyographic (EMG) signals consistent with those acquired in a clinical setting is described. Signals are generated using a model constructed to closely resemble the physiology and morphology of skeletal muscle, combined with line source models of commonly used needle electrodes positioned in a way consistent with clinical studies. The validity of the simulation routines is demonstrated by comparing values of statistics calculated from simulated signals with those from clinical EMG studies of normal subjects. The simulated EMG signals may be used to explore the relationships between muscle structure and activation and clinically acquired EMG signals. The effects of motor unit (MU) morphology, activation, and neuromuscular junction activity on acquired signals can be analyzed at the fiber, MU and muscle level. Relationships between quantitative features of EMG signals and muscle structure and activation are discussed.