Time-frequency parameters of the surface myoelectric signal forassessing muscle fatigue during cyclic dynamic contractions

The time-dependent shift in the spectral content of the surface myoelectric signal to lower frequencies has proven to be a useful tool for assessing localized muscle fatigue. Unfortunately, the technique has been restricted to constant-force, isometric contractions because of limitations in the processing methods used to obtain spectral estimates. A novel approach is proposed for calculating spectral parameters from the surface myoelectric signal during cyclic dynamic contractions. The procedure was developed using Cohen class time-frequency transforms to define the instantaneous median and mean frequency during cyclic dynamic contractions. Changes in muscle length, force, and electrode position contribute to the nonstationarity of the surface myoelectric signal. These factors, unrelated to localized fatigue, can be constrained and isolated for cyclic dynamic contractions, where they are assumed to be constant for identical phases of each cycle. Estimation errors for the instantaneous median and mean frequency are calculated from synthesized signals. It is shown that the instantaneous median frequency is affected by an error slightly lower than that related to the instantaneous mean frequency. In addition, we present a sample application to surface myoelectric signals recorded from the first dorsal interosseous muscle during repetitive abduction/adduction of the index finger against resistance. Results indicate that the variability of the instantaneous median frequency is related to the repeatability of the biomechanics of the exercise.     

Enhancement of spectral analysis of myoelectric signals duringstatic contractions using wavelet methods

In this paper, we introduce wavelet packets as an alternative method for spectral analysis of surface myoelectric (ME) signals. Both computer synthesized and real ME signals are used to investigate the performance. Our simulation results show that wavelet packet estimate has slightly less mean square error (MSE) than Fourier method, and both methods perform similarly on the real data. Moreover, wavelet packets give us some advantages over the traditional methods such as multiresolution of frequency, as well as its potential use for effecting time-frequency decomposition of the nonstationary signals such as the ME signals during dynamic contractions. We also introduce wavelet shrinkage method for improving spectral estimates by significantly reducing the MSE's for both Fourier and wavelet packet methods.     

AR modeling of myoelectric interference signals during a rampcontraction

The authors investigated the time-varying behavior of the autoregressive (AR) parameters in a myoelectric (ME) signal detected during a linear force increasing contraction. The AR parameters of interest mere the reflection coefficients, the AR model spectrum, and the prediction errors. The authors used well-conditioned ME signals for which the complete time record of the motor units firings was available. In addition, the influence of the recruitment of a new motor unit, the conduction velocity of action potentials, and additive broad-band noise were investigated using simulated ME signals. The simulated ME signals were constructed from a selected group of the available motor unit action potential trains. The results revealed that, as the contraction progressed, the AR parameters displayed a time-varying behavior which coincided with the recruitment of newly recruited motor units whose spectrum of the waveform differed from that of the rest of the ME signal. This property of the AR parameters was obscured by the presence of broad-band noise and low-amplitude motor unit action potentials, both of which are more pronounced during low-level force contractions     

多维非平稳信号的时频分析方法研究

时频分析方法能够同时描述信号在时间和频率域的能量密度与分布情况,为非平稳信号处理提供了有力的工具。文中对非平稳信号的双线性时频分析方法进行了讨论,分析了几种固定核函数的Cohen类分布在典型非平稳信号时频分析中的优缺点;详细讨论并实现了多维信号的Cohen类分布,比较了几种固定核函数的Cohen类分布分析多维信号时在抑制交叉项、自项分辨率保持方面的优缺点与核函数参数选择问题。     

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.     

基于稀疏重构的跳频信号时频分析方法

针对现有时频分析方法存在噪声抑制能力弱、时频聚集性不强的缺点,提出了一种基于稀疏重构的跳频信号时频分析方法来获取清晰的、高聚集度的时频图。首先根据惩罚函数的思想建立了跳频信号无约束的稀疏重构模型;然后理论分析了罚函数因子的取值标准;最后用近似l0范数算法求解得出跳频信号的时频图。仿真结果表明该算法能够有效地获取跳频信号的时频图。     

Wavelet-based noise removal for biomechanical signals: a comparative study

The purpose of this paper is to present wavelet-based noise removal (WBNR) techniques to remove noise from biomechanical acceleration signals obtained from numerical differentiation of displacement data. Manual and semiautomatic methods were used to determine thresholds for both orthogonal and biorthogonal filters. This study also compares the performance of WBNR approaches with four automatic conventional noise removal techniques used in biomechanics. The conclusion of this work is that WBNR techniques are very effective in removing noise from differentiated signals with sharp transients while leaving these transients intact. For biomechanical signals with certain characteristics, WBNR techniques perform better than conventional methods, as indicated by quantitative merit measures.     

块稀疏贝叶斯模型下的跳频信号时频分析

针对传统时频分析方法存在的时频聚集性差以及交叉项干扰的问题,本文将接收到的跳频信号进行分割,构建时频稀疏模型,利用模型中的统计特性和结构特性采用块稀疏贝叶斯学习算法对跳频信号的时频图进行重构,在不需知道稀疏度和噪声强度的情况下,得到了高精度的时频图。但是由于算法在高维参数空间进行参数估计时复杂度较高,本文采用近似替换的方法对该算法进行改进,将高维参数空间转换到原始参数空间计算,大大减少了算法的复杂度,仿真结果表明改进算法在低信噪比的情况下能有效的得到跳频信号的高精度时频图且复杂度大大降低。      

Surface myoelectric signal analysis: dynamic approaches for change detection and classification

Toward the goal of elbow and wrist prostheses control by characterizing events in surface myoelectric signals, this paper presents a dynamic method to simultaneously detect and classify such events. Dynamic cumulative sum of local generalized likelihood ratios using wavelet decomposition of the myoelectric signal is used for on-line detection. Frequency as well as energy changes are detected with this hybrid approach. Classification is composed of using multiresolution wavelet analysis and autoregressive modeling to extract signal features while polynomial classifiers are used for pattern modeling and matching. The results of detecting and classifying four elbow and wrist movements show that, in average, 91% of the events are correctly detected and classified using features obtained from multiresolution wavelet analysis while 95% accuracy is achieved with AR modeling. The classification accuracy decreases, however, if short prostheses response delay is desired. This paper also shows that the performance of the polynomial classifiers is better than that of the commonly used neural networks since it gives higher classification accuracy and consistent classification outcomes. In comparison to the well known support vector machine classification, the polynomial classifier gives similar results without the need to optimize and search for classifier parameters.     

基于图像处理技术的雷达辐射源信号时频特性分析

针对常用时频分析方法对多分量雷达辐射源信号(RES)分析和处理的不足,提出一种基于图像处理技术的多分量RES时频特性分析方法.该方法通过时频分布图的平滑滤波、阈值处理和基于形态学细化等算法来提取RES自分量,在有效抑制噪声的同时,能够得到具有高分辨率的多分量RES时频图.仿真实验表明,该方法既克服了常用时频分析方法的不足,又优于时频重排方法对多分量RES的时频特性分析.     

The application of neural networks to myoelectric signal analysis:a preliminary study

Two neural network implementations are applied to myoelectric signal (MES) analysis tasks. The motivation behind this research is to explore more reliable methods of deriving control for multidegree of freedom arm prostheses. A discrete Hopfield network is used to calculate the time series parameters for a moving average MES model. It is demonstrated that the Hopfield network is capable of generating the same time series parameters as those produced by the conventional sequential least squares (SLS) algorithm. Furthermore, it can be extended to applications utilizing larger amounts of data, and possibly to higher order time series models, without significant degradation in computational efficiency. The second neural network implementation involves using a two-layer perceptron for classifying a single site MES based on two features, specifically the first time series parameter, and the signal power. Using these features, the perceptron is trained to distinguish between four separate arm functions. The two-dimensional decision boundaries used by the perceptron classifier are delineated. It is also demonstrated that the perceptron is able to rapidly compensate for variations when new data are incorporated into the training set. This adaptive quality suggests that perceptrons may provide a useful tool for future MES analysis.     

Independence of myoelectric control signals examined using a surface EMG model

The detection volume of the surface electromyographic (EMG) signal was explored using a finite-element model, to examine the feasibility of obtaining independent myoelectric control signals from regions of reinnervated muscle. The selectivity of the surface EMG signal was observed to decrease with increasing subcutaneous fat thickness. The results confirm that reducing the interelectrode distance or using double-differential electrodes can increase surface EMG selectivity in an inhomogeneous volume conductor. More focal control signals can be obtained, at the expense of increased variability, by using the mean square value, rather than the root mean square or average rectified value.     

Alignment methods for averaging of high-resolution cardiac signals:a comparative study of performance

Accurate signal estimation by means of coherent averaging techniques needs temporal alignment methods. A known low-pass filtering effect is yielded when alignment errors are present. This is very critical in the estimation of low-level high-frequency potentials in high-resolution ECG analysis. A comparative study of the performance of three alignment methods (the double-level method, a new time-delay estimation method based on normalized integrals, and matched filtering) is presented in this paper. A real signal and additive random noise for several signal-to-noise ratios (SNR's) are selected to make an ensemble of computer-simulated beats. The relation between the standard deviation of temporal misalignment versus SNR is discussed. A second study with real ECG signals is also presented. Several morphologies of QRS and P waves are tested. The results are in agreement with the computer simulation study. Nevertheless, the power spectrum of the noise process can affect the results. Matched filter estimation has been tested in the presence of power line interference (50 Hz), with poor results. An application of the three alignment methods as a function of the SNR is proposed. The new time-delay estimation method has been observed to be robust, even in the presence of nonwhite noise.     

Time-frequency detection and analysis of wheezes during forced exhalation

The objective of the present work was to detect and analyze wheezes by means of a highly sensitive time-frequency algorithm. Automatic measurements were compared with clinical auscultation for forced exhalation segments from 1.2 to 0 liters/second (l/s). Sensitivities between 100% and 71%, as a function of flow level related to wheezing segments detection, were achieved. Time-frequency wheeze parameters were measured for the flow range from 1.2 to 0.2 l/s. Wheezes were detected in both analyzed groups; asthmatics (N = 16) and control subjects (N = 15). Significant differences between groups were found for the mean number of wheezes detected at basal condition (p = 0.0003). Frequency parameter differences were also significant (0.0112 < p < 0.0307). All these parameters were also studied after applying a bronchodilator drug (Terbutaline). Significant differences between patient groups were found when studying the changes in the number of wheezes for each patient (p = 0.0195). Finally, limited bandwidth parameters, which measure the bronchodilator response, were also studied.     

Time-frequency characterization of interdependencies in nonstationary signals: application to epileptic EEG

For the past decades, numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between electroencephalographic (EEG) signals. This interdependency parameter, which may be defined in various ways, is often used to characterize a functional coupling between different brain structures or regions during either normal or pathological processes. In this paper, we focus on the time-frequency characterization of the interdependency between signals. Particularly, we propose a novel estimator of the linear relationship between nonstationary signals based on the cross correlation of narrow band filtered signals. This estimator is compared to a more classical estimator based on the coherence function. In a simulation framework, results show that it may exhibit better statistical performances (bias and variance or mean square error) when a priori knowledge about time delay between signals is available. On real data (intracerebral EEG signals), results show that this estimator may also enhance the readability of the time-frequency representation of relationship and, thus, can improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).     

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.     

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.     

Optimized wavelets for blind separation of nonstationary surface myoelectric signals

Surface electromyography (EMG) signals detected over the skin surface may be mixtures of signals generated by many active muscles due to poor spatial selectivity of the recording. In this paper, we propose a new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures. The method is based on whitening of the observations and rotation of the whitened observations. The rotation is performed by joint diagonalization of a set of spatial wavelet distributions (SWDs). The SWDs depend on the selection of the mother wavelet which can be defined by unconstrained parameters via the lattice parameterization within the multiresolution analysis framework. As the sources are classically supposed to be mutually uncorrelated, the design parameters of the mother wavelet can be blindly optimized by minimizing the average (over time lags) cross correlation between the estimated sources. The method was tested on simulated and experimental surface EMG signals and results were compared with those obtained with spatial time-frequency distributions and with second-order statistics (only spectral information). On a set of simulated signals, for 10-dB signal-to-noise ratio (SNR), the cross-correlation coefficient between original and estimated sources was 0.92 +/- 0.07 with wavelet optimization, 0.74 +/- 0.09 with the wavelet leading to the poorest performance, 0.85 +/- 0.07 with Wigner-Ville distribution, 0.86 +/- 0.07 with Choi-Williams distribution, and 0.73 +/- 0.05 with second-order statistics. In experimental conditions, when the flexor carpi radialis and pronator teres were concomitantly active for 50% of the time, crosstalk was 55.2 +/- 10.0% before BSS and was reduced to 15.2 +/- 6.3% with wavelet optimization, 30.1 +/- 15.0% with the worst wavelet, 28.3 +/- 12.3% with Wigner-Ville distribution, 26.2 +/- 12.0% with Choi-Williams distribution, and 35.1 +/- 15.5% with second-order statistics. In conclusion, the proposed approach resulted in better performance than previous methods for the separation of nonstationary myoelectric signals.     

Time-frequency analysis of transients

A new representation of electromagnetic transients associated with perfectly-conducting finite-size objects is proposed. Our proposal is motivated by the fact that both time representation and frequency representation of suchlike transients are not fully satisfactory. We examine a tool for imaging transients in the time-frequency domain, namely the Page instantaneous spectrum. This is illustrated in a number of examples with pulse excited dipoles that the Page spectrum leads to readable picture of time-frequency evolution of the transient process.