Spectral Analysis of Surface Motor Unit Action Potentials and Surface Interference Electromyogram

Surface interference electromyograms (EMG's) were recorded from the tibial muscle of a healthy subject during 50 percent maximal contraction and single motor unit action potentials (MUAP's) were isolated by averaging from the interference pattern. The formation of the EMG was simulated by summing isolated MUAP's according to the statistical properties of the corresponding motor unit discharges. Power spectral density functions (PSDF's) were finally computed for single MUAP's as well as for simulated and experimental EMG's and compared with each other.     

Single site electromyograph amplitude estimation

Previous investigators have experimentally demonstrated and/or analytically predicted that temporal whitening of the surface electromyograph (EMG) waveform prior to demodulation improves the EMG amplitude estimate. However, no systematic study of the influence of various whitening filters upon amplitude estimate performance has been reported. The authors describe a phenomenological mathematical model of a single site of the surface EMG waveform and reports on experimental studies which examined the performance of several temporal whitening filters. Surface EMG waveforms were sampled 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). A moving average root mean square estimator (245 ms window) provided an average±standard deviation (A±SD) SNR of 10.7±3.3 for the individual recordings. Temporal whitening with one fourth-order whitening filter designed per site improved the A±SD SNR to 17.6±6.0     

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.     

Influence of smoothing window length on electromyogram amplitudeestimates

A systematic, experimental study of the influence of smoothing window length on the signal-to-noise ratio (SNR) of electromyogram (EMG) amplitude estimates is described. Surface EMG waveforms were sampled during nonfatiguing, constant-force, constant-angle contractions of the biceps or triceps muscles, over the range of 10%-75% maximum voluntary contraction. EMG amplitude estimates were computed with eight different EMG processor schemes using smoothing length durations spanning 2.45-500 ms. An SNR was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Over these window lengths, average ± standard deviation SNR's ranged from 1.4±0.28 to 16.2±5.4 for unwhitened single-channel EMG processing and from 3.2±0.7 to 37.3±14.2 for whitened, multiple-channel EMG processing (results pooled across contraction level). It was found that SNR increased with window length in a square root fashion. The shape of this relationship was consistent with classic theoretical predictions, however none of the processors achieved the absolute performance level predicted by the theory. These results are useful in selecting the length of the smoothing window in traditional surface EMG studies. In addition, this study should contribute to the development of EMG processors which dynamically tune the smoothing window length when the EMG amplitude is time varying     

Fatigue analysis of the surface EMG signal in isometric constant force contractions using the averaged instantaneous frequency

The averaged instantaneous frequency (AIF) is proposed as an alternative method for the frequency analysis of surface electromyography (EMG) in the study of muscle fatigue during sustained, isometric muscle contractions. Results from performance analysis using experimental EMG signals demonstrate the low variability of the proposed frequency variable. Indeed, the AIF measure is shown to perform significantly better than the widely used mean and median frequency variables, in terms of robustness to the length of the analysis window.     

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.     

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     

Time-frequency analysis of myoelectric signals during dynamic contractions: a comparative study

In this paper, we introduce the nonstationary signal analysis methods to analyze the myoelectric (ME) signals during dynamic contractions by estimating the time-dependent spectral moments. The time-frequency analysis methods including the short-time Fourier transform, the Wigner-Ville distribution, the Choi-Williams distribution, and the continuous wavelet transform were compared for estimation accuracy and precision on synthesized and real ME signals. It is found that the estimates provided by the continuous wavelet transform have better accuracy and precision than those obtained with the other time-frequency analysis methods on simulated data sets. In addition, ME signals from four subjects during three different tests (maximum static voluntary contraction, ramp contraction, and repeated isokinetic contractions) were also examined.     

Analysis and simulation of changes in EMG amplitude during high-level fatiguing contractions

Changes in surface electromyographic (EMG) amplitude during sustained, fatiguing contractions are commonly attributed to variations in muscle fiber conduction velocity (MFCV), motor unit firing rates, transmembrane action potentials and the synchronization or recruitment of motor units. However, the relative contribution of each factor remains unclear. Analytical relationships relating changes in MFCV and mean motor unit firing rates to the root mean square (RMS) and average rectified (AR) value of the surface EMG signal are derived. The relationships are then confirmed using model simulation. The simulations and analysis illustrate the different behaviors of the surface EMG RMS and AR value with changing MFCV and firing rate, as the level of motor unit superposition varies. Levels of firing rate modulation and short-term synchronization that, combined with variations in MFCV, could cause changes in EMG amplitude similar to those observed during sustained isometric contraction of the brachioradialis at 80% of maximum voluntary contraction were estimated. While it is not possible to draw conclusions about changes in neural control without further information about the underlying motor unit activation patterns, the examples presented illustrate how a combined analytical and simulation approach may provide insight into the manner in which different factors affect EMG amplitude during sustained isometric contractions.     

E-OBS网络中一种基于优先级的抢占窗口机制

为了有效地降低突发包的丢失率和保证网络的服务质量,提出了模拟光突发交换网络中一种基于优先级的抢占窗口机制.该机制在模拟光突发交换核心路由器的控制信道上设置抢占窗口,以此来决定是否允许高优先级突发包抢占低优先级突发包.冲突发生时,系统判断高优先级突发包对应的控制包的到达时间是否满足抢占条件,如果满足抢占条件,则允许高优先...     

Group-Scheduling for Multi-Service Optical Burst Switching (OBS) Networks

We propose a new burst scheduling mechanism for Optical Burst-Switched (OBS) networks. The new approach is made possible by gathering data bursts into groups and performing the scheduling decision for each group collectively. In OBS group-scheduling, bursts will not be considered for scheduling until a pre-defined time period elapses, during which the group of burst header packets would be gathered. By transforming a set of data bursts into a set of corresponding time intervals, the problem of scheduling these bursts is transformed into a combinatorial optimization problem. Graph algorithms are applied to obtain the maximum number of non-overlapping bursts. The proposed OBS group-scheduling scheme is shown to improve the performance of OBS networks over existing scheduling schemes in terms of burst loss probability and channel utilization. With an extension through a sequential optimization, using a Branch-and-Bound technique, the proposed scheme can support multiple classes of service. It is shown that the new scheduling approach has several desired characteristics including fairness and service differentiability among classes in terms of burst loss probability and channel utilization.     

Reducing muscle fatigue in FES applications by stimulating withN-let pulse trains

Applications of electrical stimulation for restoration of functional movements such as standing, gait, and grasp have always been hindered by the rapid fatigue of stimulated muscle. This paper describes an experimental investigation of stimulation with N-lets (a set of N closely spaced stimulation pulses) as a means of producing contractions with improved fatigue characteristics. Experiments were conducted on 27 able-bodied and four SCI human subjects using surface stimulation of the quadriceps muscle to produce isometric knee joint torque. Based upon evidence from the literature on muscle fatigue, parameters of the N-let trains for N=1-6 were optimized to produce the most force per pulse. The results demonstrated that: 1) nonlinear summation of the twitch response occurs in human subjects with N-let surface stimulation; 2) for most subjects, doublet stimulation (N=2) with a pulse interval of about 5 ms produced the maximum torque-time integral per pulse of the resulting twitch; and 3) on average, optimal N-let stimulation resulted in a 36% increase in isometric torque tracking when compared to traditional singlet stimulation. The results have immediate implications for alleviating the problem of premature fatigue during functional electrical stimulation     

基于短时傅里叶变换分析超短光脉冲的传输特性

短时傅里叶变换可将1维时域或频率信号扩展到时间-频率的2维平面.为了研究了光纤中的色散效应与脉冲的初始啁啾对信号传输的影响,采用短时傅里叶变换理论进行了分析.与传统傅里叶变换相比,短时傅里叶变换可以更直观地描述光纤的色散效应与脉冲的初始啁啾如何影响信号的时域与频率的传输特性;此外,从短时傅里叶变换的时频分析图还可以很清晰地观察到在脉冲传输过程中,由色散效应与脉冲的初始啁啾所诱导的新的频率啁啾的演化规律.结果表明,短时傅里叶变换克服了传统的傅里叶变换法只能单独在频率或时域中比较信号的瞬态特性缺点,为分析光纤中脉冲信号的传输提供了一种新途径.     

Motor Unit Firing Rate During Static Contraction Indicated by the Surface EMG Power Spectrum

In this study, power spectral density functions (PSDF's) were computed of interference EMG of various facial and jaw-elevator muscles during nonfatiguing submaximal static contractions, recorded with surface electrodes. A distinct peak was found in the PSDF's in the frequency region below 40 Hz. It was shown that the peak was due to genuine EMG activity and that it could not be considered as an artifact, which was caused by electrode displacements during contraction. An increase of contraction strength resulted in a shift of the peak to higher frequencies and a decrease of peak amplitude relative to the power spectral estimates above 40 Hz, which were shown to be determined by the shape of the motor unit (MU) action potentials. In accordance with mathematical models of the EMG PSDF, it was demonstrated that the peak indicates the dominant firing rate of the sampled MU's. Our results suggest that this can be defined as the firing rate of the first recruited low-threshold MU's, which may be expected to dominate the interference EMG signal because of their preponderance in number. The data further suggest that the peak can be more readily observed in PSDF's of facial and jaw-elevator muscles than in PSDF's of limb muscles. This might be related to differences in MU firing statistics.     

突发信号盲存在性检测的两种算法

本文从频率域和广义频率域研究了复数高斯白噪声信道中突发信号的存在性检测问题,分别提出了基于频率域短时傅氏变换幅度谱熵和基于广义频率域奇异值分解的检测算法,并与时间域的短时能量算法进行了比较.仿真结果表明谱熵法具有较好的鲁棒性,特别是在低信噪比时能够获得较高的检测概率,并且受突发信号调制方式等参数的影响较小.奇异值算法与短时能量法相比更适用于采用QAM调制的突发信号.     

The S-transform using a new window to improve frequency and time resolutions

The S-transform presents arbitrary time series as localized invertible time–frequency spectra. This transformation improves the short-time Fourier transform and the wavelet transform by merging the multiresolution and frequency-dependent analysis properties of wavelet transform with the absolute phase retaining of Fourier transform. The generalized S-transform utilizes a combination of a Fourier transform kernel and a scalable-sliding window. The common S-transform applies a Gaussian window to provide appropriate time and frequency resolution and minimizes the product of these resolutions. However, the Gaussian S-transform is unable to obtain uniform time and frequency resolution for all frequency components. In this paper, a novel window based on the $t$ student distribution is proposed for the S-transform to achieve a more uniform resolution. Simulation results show that the S-transform with the proposed window provides in comparison with the Gaussian window a more uniform resolution for the entire time and frequency range. The result is suitable for applications such as spectrum sensing.     

A unified approach to short-time Fourier analysis and synthesis

Two distinct methods for synthesizing a signal from its short-time Fourier transform have previously been proposed. We call these methods the filter-bank summation (FBS) method and the overlap add (OLA) method. Each of these synthesis techniques has unique advantages and disadvantages in various applications due to the way in which the signal is reconstructed. In this paper we unify the ideas behind the two synthesis techniques and discuss the similarities and differences between these methods. In particular, we explicitly show the effects of modifications made to the short-time transform (both fixed and time-varying modifications are considered) on the resulting signal and discuss applications where each of the techniques would be most useful The interesting case of nonlinear modifications (possibly signal dependent) to the short-time Fourier transform is also discussed. Finally it is shown that a formal duality exists between the two synthesis methods based on the properties of the window used for obtaining the short-time Fourier transform.     

Nonstationarity broadening reduction in pulsed Doppler spectrummeasurements using time-frequency estimators

The spectral width of Doppler signals is used as measure of lesion-induced flow disturbance. Its estimation accuracy is compromised using the conventional short-term Fourier transform (STFT) since this method implicitly assumes signal stationarity during the signal window while the Doppler signals from arteries are markedly nonstationary. The Wigner-Ville (WVD), Choi-Williams (CWD) and Bessel distributions (BD), specifically designed for nonstationary signals, have been optimized for spectral width estimation accuracy and compared to the STFT under different signal to noise ratios using simulated Doppler signals of known time-frequency characteristics. The optimum parameter values for each method were determined as a Hanning window duration of 10 ms for the STFT, 40 ms for the WVD and CWD and 20 ms for the BD and dimensionless time-frequency smoothing constant values of five in the CWD and two in the BD. Thresholding was used to reduce the effect of cross terms and side lobes in the WVD and BD. With no added noise the WVD gave the lowest estimation error followed by the CWD. At signal-to-noise ratios (SNRs) of 10 dB and 20 dB the CWD and BD had similar errors and were markedly better than the other estimators. Overall the CWD gave the best performance     

基于窗口的光突发交换调度算法

针对光突发交换网(OBS)中的资源竞争和QoS支持等问题，提出了一种新型的基于窗口的调度算法。该算法利用边缘节点的电缓存，对调度窗口中的突发数据包进行批量BORA调度，可以有效地降低网络中发生资源竞争的概率；同时调度窗口中的优先级策略还可以进一步增强QoS。网络仿真结果表明，通过选择合适的调度窗口和最大允许时延，该调度算法在0．8的网络负载下使得高优先级突发数据包的阻塞率下降一个量级，信道利用率提高3．5％。     

E-OBS网络中一种基于窗口的资源预留机制

为了有效地降低突发包的阻塞率和保证网络的服务质量,提出了模拟光突发交换（E-OBS）网络中一种偏置时间连续可变的基于窗口资源预留机制。在E-OBS核心路由器的控制信道（CC）上设置资源预留窗口,以此决定是否允许控制包为相应的突发包预留链路资源,并且给出了该机制下关于阻塞概率的近似方程式。仿真结果表明,适当增加资源预留窗...