Spectrum of the nonstationary electromyographic signal modelled with integral pulse frequency modulation and its application to estimating neural drive information

The spectrum of nonstationary electromyographic signal (EMG) is investigated, from which the error for neural drive information estimation from nonstationary EMG is studied in terms of signal-to-noise ratio (SNR), in analytical, numerical simulation, and experimental work. The signal refers to the neural drive information embedded within the nonstationary EMG, and noise refers to other portions of EMG that induce error in the estimation. The analytical expressions for the SNRs of force-modulated EMG with both single and multiple motor units (MU) are derived based on a sinusoidal integral pulse frequency modulation (IPFM) model. It is shown that the previously developed SNR expressions for stationary (unmodulated) EMG are special cases of the formulas presented here. The SNR results obtained from numerical simulated EMG agree very well with the analytical result. Results from nonstationary (modulated) surface EMG obtained from seven subjects also match the analytical and simulation results reasonably well. The results obtained from this work establish an analytical framework in studying and estimating the neural drive information contained in the EMG in the context of anisotonic and isometric contractions. Through the analytical study, the effects of different physiological parameters are identified, thus providing theoretical guidelines for developing advanced signal processing methods for nonstationary EMG in applications such as prosthesis control.     

Relationship Between Time- and Frequency-Domain Analyses of Angular Head Movements in the Squirrel Monkey

We used the three-dimensional magnetic search-coil recording technique to study the range of active angular head movements made by squirrel monkeys. There were two goals in this study: (1) to determine the range of angular velocities and accelerations as well as the bandwidth and other frequency characteristics of active head movements and (2) to compare analyses of transients of velocity and acceleration that are studied by residual analysis, Fourier transform, and wavelet transform of the head velocity signal.The residual analysis showed that the shape and duration of the transients affected the bandwidth. During the time after the head had begun to accelerate, the frequency content of the head movement extended into the range of 6 to 12 Hz. When considering all three planes of rotation, approximately 75% of the transients had peak acceleration between 2,000 and 10,000 deg/s² and a peak velocity of 50 to 400 deg/s. A peak acceleration of >10,000 deg/s² was recorded in 10% of the transients.These findings indicate that active head movements in squirrel monkeys cover a higher range of frequencies, accelerations, and velocities than have typically been used in previous eye-movement and neuronal studies of the reflexes that control gaze. We further conclude that the choice of a method for analyzing transient, time-varying biological signals is dependent on the desired information. Residual analysis provides detailed resolution in the time domain, but estimation of the frequency content of the signal is dependent on the portions selected for analysis and the choice of filters. Fourier transform provides a representation of the power spectrum in the frequency domain but without any inherent temporal resolution. We show that the wavelet transform, a novel method as applied to the signal analysis goals of this study, is the most useful technique for relating time- and frequency-domain information during a continuous signal.     

Widefield multifrequency fluorescence lifetime imaging using a two‐tap complementary metal‐oxide semiconductor camera with lateral electric field charge modulators

Widefield frequency‐domain fluorescence lifetime imaging microscopy (FD‐FLIM) measures the fluorescence lifetime of entire images in a fast and efficient manner. We report a widefield FD‐FLIM system based on a complementary metal‐oxide semiconductor camera equipped with two‐tap true correlated double sampling lock‐in pixels and lateral electric field charge modulators. Owing to the fast intrinsic response and modulation of the camera, our system allows parallel multifrequency FLIM in one measurement via fast Fourier transform. We demonstrate that at a fundamental frequency of 20 MHz, 31‐harmonics can be measured with 64 phase images per laser repetition period. As a proof of principle, we analyzed cells transfected with Cerulean and with a construct of Cerulean‐Venus that shows Förster Resonance Energy Transfer at different modulation frequencies. We also tracked the temperature change of living cells via the fluorescence lifetime of Rhodamine B at different frequencies. These results indicate that our widefield multifrequency FD‐FLIM system is a valuable tool in the biomedical field.      

Frequency characteristics of signals and instrumentation: implication for EMG biofeedback studies

Signals can be analyzed in either the time or frequency domain. In the time domain, the analysis consists of manipulating and measuring one or more characteristics of the signal that may vary with time. One can, for instance, rectify a signal, filter it, calculate its mean value, display the histogram of its amplitude, and so forth. Frequency analysis is less well understood because it requires a lengthy mathematical treatment most easily done by computer. However, it gives exclusive information on a signal. For instance, when the frequency content of a signal is known, it is easy to specify which characteristics an amplifier must have in order to amplify the signal without distortion, or to set the cutoff frequencies of filters to eliminate noise. Also, in many circumstances, frequency spectra are more easily interpreted than the original raw data. Such is the case with the EMG where the random aspect of the signal makes some form of processing (i.e., rectification, filtering, etc.) necessary, but not always as meaningful as we would like. Thus we present here the principal characteristics of frequency analysis, and discuss its usefulness in analyzing EMG signals and its application to biofeedback, clinical practice, and research.     

Time and frequency domain responses of the mechanomyogram and electromyogram during isometric ramp contractions: a comparison of the short-time Fourier and continuous wavelet transforms.

The purposes of this study were to examine the mechanomyographic (MMG) and electromyographic (EMG) time and frequency domain responses of the vastus lateralis (VL) and rectus femoris (RF) muscles during isometric ramp contractions and compare the time-frequency of the MMG and EMG signals generated by the short-time Fourier transform (STFT) and continuous wavelet transform (CWT). Nineteen healthy subjects (mean+/-SD age=24+/-4 years) performed two isometric maximal voluntary contractions (MVCs) before and after completing 2-3, 6-s isometric ramp contractions from 5% to 100% MVC with the right leg extensors. MMG and surface EMG signals were recorded from the VL and RF muscles. Time domains were represented as root mean squared amplitude values, and time-frequency representations were generated using the STFT and CWT. Polynomial regression analyses indicated cubic increases in MMG amplitude, MMG frequency, and EMG frequency, whereas EMG amplitude increased quadratically. From 5% to 24-28% MVC, MMG amplitude remained stable while MMG frequency increased. From 24-28% to 76-78% MVC, MMG amplitude increased rapidly while MMG frequency plateaued. From 76-78% to 100% MVC, MMG amplitude plateaued (VL) or decreased (RF) while MMG frequency increased. EMG amplitude increased while EMG frequency changed only marginally across the force spectrum with no clear deflection points. Overall, these findings suggested that MMG may offer more unique information regarding the interactions between motor unit recruitment and firing rate that control muscle force production during ramp contractions than traditional surface EMG. In addition, although the STFT frequency patterns were more pronounced than the CWT, both algorithms produced similar time-frequency representations for tracking changes in MMG or EMG frequency.     

Acoustic pattern recognition in a grasshopper: processing in the time or frequency domain?

Males of the grasshopper Chorthippus biguttulus produce songs which consist of the stereotyped and rhythmic iteration of a sound unit (termed syllable) separated by distinct syllable pauses. Virgin females respond to this signal, and to similar artificial signals, with song phrases of their own. In behavioural experiments the response probability of virgin females can be measured with artificial acoustic stimuli. The stimuli consisted of an amplitude modulated noise the envelope of which was altered. We investigated several hypotheses on the mechanisms of conspecific song recognition with special emphasis on the question whether recognition occurs in the frequency domain or in the time domain. (1) Females of Ch. biguttulus required only the first five Fourier components of the envelope function (corresponding to 50 Hz for a fundamental frequency of 10 Hz) to detect the syllable/pause structure. In addition, they detected small gaps within syllables if the signal contained at least ca. 15 Fourier components (corresponding to a frequency of 150 Hz). Further experiments showed that the correct phase information of the Fourier components is necessary for recognition, indicating that pattern recognition is not achieved merely on the basis of band pass filtering. (2) A cross correlation between the signal and an assumed internal template yields only inconsistent predictions of the response probabilities. (3) The recognizer system probably works in the time domain, possibly by direct comparison of adjacent syllable and pause durations. It is not yet clear whether the duration of a syllable is evaluated with respect to the preceding or succeeding pause. We emphasize that the neural recognizer of the grasshopper does not only examine a signal for its similarity to an internal template, but that it also takes into account features that indicate an incorrect signal. This may be a general feature of neuronal pattern recognition systems which have been shaped by natural selection. Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Comparison of Fourier and wavelet transform procedures for examining the mechanomyographic and electromyographic frequency domain responses during fatiguing isokinetic muscle actions of the biceps brachii.

The primary purpose of the present study was to compare the fast Fourier transform (FFT) with the discrete wavelet transform (DWT) for determining the mechanomyographic (MMG) and electromyographic (EMG) center frequency [mean power frequency (mpf), median frequency (mdf), or wavelet center frequency (cf)] patterns during fatiguing isokinetic muscle actions of the biceps brachii. Seven men (mean+/-SD age=23+/-3 years) volunteered to perform 50 consecutive maximal, concentric isokinetic muscle actions of the dominant forearm flexors at a velocity of 180 degrees s(-1). Non-parametric "run" tests indicated significant (p<0.05) trends in the MMG and EMG signals for the 5th, 25th, and 45th muscle actions for all subjects, thereby confirming non-stationarity of the MMG and EMG signals. There were significant (p<0.05) correlations among the average normalized mpf, mdf, and cf values for contractions 1-50 for both MMG (r=0.671-0.935) and EMG (r=0.956-0.987). Polynomial regression analyses demonstrated quadratic decreases in normalized MMG mpf (R2=0.439), MMG mdf (R2=0.258), MMG cf (R2=0.359), EMG mpf (R2=0.952), EMG mdf (R2=0.914) and EMG cf (R2=0.888) across repetitions. The primary finding of this study was the similarity in the mpf, mdf, and cf patterns for both MMG and EMG, which suggested that, despite the concerns over non-stationarity, Fourier based methods are acceptable for determining the patterns for normalized MMG and EMG center frequency during fatiguing dynamic muscle actions at moderate velocities.     

Frequency characteristics of signals and instrumentation: Implication for EMG biofeedback studies

Signals can be analyzed in either the time or frequency domain. In the time domain, the analysis consists of manipulating and measuring one or more characteristics of the signal that may vary with time. One can, for instance, rectify a signal, filter it, calculate its mean value, display the histogram of its amplitude, and so forth. Frequency analysis is less well understood because it requires a lengthy mathematical treatment most easily done by computer. However, it gives exclusive information on a signal. For instance, when the frequency content of a signal is known, it is easy to specify which characteristics an amplifier must have in order to amplify the signal without distortion, or to set the cutoff frequencies of filters to eliminate noise. Also, in many circumstances, frequency spectra are more easily interpreted than the original raw data. Such is the case with the EMG where the random aspect of the signal makes some form of processing (i.e., rectification, filtering, etc.) necessary, but not always as meaningful as we would like. Thus we present here the principal characteristics of frequency analysis, and discuss its usefulness in analyzing EMG signals and its application to biofeedback, clinical practice, and research.The authors acknowledge the technical assistance of F. Kemp, M. Goyette, and C. Goulet. T. Milner kindly reviewed the final version of the text. The preparation of this paper was supported through funds from Health and Welfare Canada (NHRDP) and the Centre de recherche, Institut de réadaptation de Montréal.     

Physiological evidence for central modulation of voice tremor

The present report presents an attempt to define the physiological parameter used to describe “voice tremor” in psychological stress evaluating machines, and to find its sources. This parameter was found to be a low frequency (5–20 Hz) random process which frequency modulates the vocal cord waveform and (independently) affects the frequency range of the third speech formant. The frequency variations in unstressed speakers were found to be the result of forced muscular undulations driven by central nervous signals and not of a passive resonant phenomenon. In this paper various physiological and clinical experiments which lead to the above conclusions are discussed. a) It is shown that induced muscular activity in the vocal tract and vocal cord regions can generate tremor in the voice. b) It is shown that relaxed subjects exhibit significant tremor correlation between spontaneously generated speech and EMG, with the EMG leading the speech tremor. c) Tremor in the electrical activity recorded from muscles overlapping vocal tract area was correlated with third formant demodulated signal and vocal cord demodulated pitch tremor was correlated with first formant demodulated tremor. d) Enhanced tremor was found in Parkinson patients and diminished tremor in patients with some traumatic brain injuries.     

Wavelet transform as a potential tool for ECG analysis and compression

The recently introduced wavelet transform is a member of the class of time-frequency representations which include the Gabor short-time Fourier transform and Wigner-Ville distribution. Such techniques are of significance because of their ability to display the spectral content of a signal as time elapses. The value of the wavelet transform as a signal analysis tool has been demonstrated by its successful application to the study of turbulence and processing of speech and music. Since, in common with these subjects, both the time and frequency content of physiological signals are often of interest (the ECG being an obvious example), the wavelet transform represents a particularly relevant means of analysis. Following a brief introduction to the wavelet transform and its implementation, this paper describes a preliminary investigation into its application to the study of both ECG and heart rate variability data. In addition, the wavelet transform can be used to perform multiresolution signal decomposition. Since this process can be considered as a sub-band coding technique, it offers the opportunity for data compression, which can be implemented using efficient pyramidal algorithms. Results of the compression and reconstruction of ECG data are given which suggest that the wavelet transform is well suited to this task.     

Subtraction of background fluorescence in multiharmonic frequency-domain fluorimetry.

Background fluorescence is a major concern in time-resolved microfluorimetry studies of biological samples. A general method for subtraction of an arbitrary background signal in measurements of lifetime and anisotropy decay by multiharmonic Fourier transform spectroscopy is presented. Multifrequency phase and modulation values are measured in parallel by transformation of digitized time-domain waveforms into the frequency domain. For subtraction of background, time-domain waveforms are acquired for emission and reference photomultipliers for sample (e.g., cell containing fluorophore) and blank (e.g., unlabeled cell). Time-domain waveforms obtained in a series of measurements (e.g., sample and blank for parallel and perpendicular orientations of an emission polarizer) are time-justified by least-squares fitting of reference channel waveforms or by phase comparison of the first Fourier harmonics of the reference channel. Background is then subtracted directly in the time domain, and the subtracted waveform is Fourier transformed to the frequency domain for analysis of lifetime or anisotropy decay. This approach yielded excellent background correction over a wide range of background intensities and decay profiles. The method was tested in cuvette fluorimetry with fluorescein and acridine orange and in fluorescence microscopy with living MDCK cells loaded with the pH indicator BCECF. Sample lifetimes and rotational parameters could be recovered accurately with greater than 50% of the signal arising from background. These results establish a direct and practical approach to subtraction of background in complex biological and chemical samples studied by frequency-domain fluorimetry.     

The effects of motor unit synchronization on the power spectrum of the electromyogram

A realistic model for two synchronized motor unit action potential trains (MUAPT) is presented in which the variability of the time difference between corresponding action potentials (hereafter denoted by delay) is taken into account. Specifically, this delay is modeled as a continuous random variable that may assume both positive and negative values.Expressions are derived for the auto- and cross-power spectra of two such trains using their relations with the auto- and cross-correlation functions, respectively, with which they form Fourier transform pairs.The results show that the auto- and the cross-power spectra of two such synchronized MUAPTs differ from the auto- and the cross-spectra of two independent MUAPTs. The contribution of the statistics of the interpulse intervals to one of the autopower spectra is smaller and the cross-power spectra no longer reduce to a Dirac -function at the origin but are now determined by the other auto-power spectrum and by the Fourier transform of the density function associated with the time difference between corresponding action potentials. As a consequence of this change in the cross-power spectra synchronization leads to an absolute increase of power at low frequencies and to a relative decrease of power at high frequencies.The results are then generalized to electromyograms (EMG) composed of more than just two MUAPTs and illustrated with simulated power spectra with which the theory shows excellent agreement.     

Prediction of "hot spots" in interleukin-2 based on informational spectrum characteristics of growth-regulating factors. Comparison with experimental data

The Resonant Recognition Model (RRM) is a theoretical method for analysis of protein and nucleotide sequences, based on the Fourier transform of the numerical representation of sequences. The amplitude spectrum of this transform is designated Informational Spectrum (IS). There are certain common frequencies in IS of growth-regulating factors. These characteristic frequencies may correlate with their roles in cell proliferation and metabolism, and in antitumor activity. IS of IL-2 has prominent characteristics in the main frequency domain of growth factors, frequency domain of antitumor factors, and frequency domain characteristic for IL-2-alpha receptor. By means of the inverse method for these 3 domains, the amino acids in the sequence of human IL-2 that may be relevant to its biological function, the so-called "hot spots", were predicted. The most probable hot spots, obtained in this way, are in the potential binding site of IL-2 to its receptor, which agrees with experimental data.     

Nonlinear time-course of lumbar muscle fatigue using recurrence quantifications

 Isometric skeletal muscle fatigue is usually assumed to be a linear process based upon the monotonic decrease in spectral frequency of the EMG. Since spectral analysis by fast Fourier transform (FFT) constitutes a linear transformation of the data, the present study was designed to reevaluate the time-course of muscle fatigue with a nonlinear tool, recurrence quantification analysis (RQA). Surface EMG recordings were obtained from the multifidus muscle of 17 human subjects during isometric posture-holding of the upper torso. The process of muscle fatigue was found to be linear for 59% of the subjects by FFT criteria, but nonlinear for 76% by RQA criteria. As a demonstrative control, both slow and fast transients occurring within a nonlinear mathematical process could be accurately depicted by RQA, but not by FFT. It is concluded that assessment of EMG patterns by nonlinear techniques can give insight into the time-course of fatiguing muscles attributed to the summation of several nonlinear and competing processes. Received: 12 November 1998 / Accepted in revised form: 29 November 1999     

基于空间频域滤波高动态光学投影层析的斑马鱼三维成像研究

本文提出了一种基于空间频率滤波的多曝光融合的高动态投影层析三维成像方法,实现了活体斑马鱼（17 mm × 4 mm,最大厚度为2.33 mm,最小厚度为0.29 mm）的三维结构成像. 通过相机采用不同曝光时间记录系列吸收图像,将每张图像取变换到频域去除低频后,将各张滤波后叠加并逆傅里叶变换回空域,对变换后的图像进行归一化处理,最终获得高动态图像. 在每个投影角度获得这种高动态吸收投影图像,进行滤波反投影算法重建,获得高动态的整条斑马鱼三维结构信息. 实验成像结果表明,这种空间频率滤波多曝光融合的高动态光学投影层析三维成像研究,可以获得复杂结构更丰富的空间信息,对斑马鱼等模式生物早期胚胎生长发育进程进行监测和定量评估有一定的应用前景.     

Characteristics of power spectrum density function of EMG during muscle contraction below 30%MVC

The aim of the study was to quantify changes in PSDF frequency bands of the EMG signal and EMG parameters such as MF, MPF and zero crossing, with an increase in the level of muscle contractions in the range from 0.5% to 30% RMS_max and to determine the frequency bands with the lowest dependency on RMS level so that this could be used in investigating muscle fatigue.Sixteen men, aged from 23 to 33 years old (mean 26.1), who participated in the study performed two force exertion tests. Fragments of EMG which corresponded to the levels of muscle contraction of 0.5%, 1%, 2.5%, 5%, 10%, 15%, 20%, 25%, 30% RMS_max registered from left and right trapezius pars descendents (TP) and left and right extensor digitorum superficialis (ED) muscles were selected for analysis. The analysis included changes in standard parameters of the EMG signal and changes in PSDF frequency bands, which occurred across muscle contraction levels. To analyze changes in PSDF across the level of muscle contraction, the spectrum was divided into six frequency bandwidths. The analysis of parameters focused on the differences in those parameters between the analyzed muscles, at different levels of muscle contraction.The study revealed that, at muscle contraction levels below 5% RMSmax, contraction level influences standard parameters of the EMG signal and that at such levels of muscle contraction every change in muscle contraction level (recruitment of additional MUs) is reflected in PSDF. The frequency band with the lowest dependency on contraction level was 76–140 Hz for which in both muscles no contraction level effect was detected for contraction levels above 5% RMS_max. The reproducibility of the results was very high, since the observations in of the left and right muscles were almost equal. The other factor, which strongly influences PSDF of the EMG signal, is probably the examined muscle structure (muscle morphology, size, function, subcutaneous layer, cross talk). It seems that low frequency bands up to 25 Hz are especially feasible for type of muscle.     

Visual saliency: a biologically plausible contourlet-like frequency domain approach

In this paper we propose a fast frequency domain saliency detection method that is also biologically plausible, referred to as frequency domain divisive normalization (FDN). We show that the initial feature extraction stage, common to all spatial domain approaches, can be simplified to a Fourier transform with a contourlet-like grouping of coefficients, and saliency detection can be achieved in frequency domain. Specifically, we show that divisive normalization, a model of cortical surround inhibition, can be conducted in frequency domain. Since Fourier coefficients are global in space, we extend to this model by conducting piecewise FDN (PFDN) using overlapping local patches to provide better biological plausibility. Not only do FDN and PFDN outperform current state-of-the-art methods in eye fixation prediction, they are also faster. Speed and simplicity are advantages of our frequency domain approach, and its biological plausibility is the main contribution of our paper.     

System analysis of Phycomyces light-growth response with gaussian white-noise test stimuli

The light-growth response of the Phycomyces sporangiophore is a transient change of elongation rate in response to changes in ambient blue-light intensity. The white-noise method of nonlinear system identification (Wiener-Lee-Schetzen theory) has been applied to this response, and the results have been interpreted by system analysis methods in the frequency domain. Experiments were performed on the Phycomyces tracking machine. Gaussian white-noise stimulus patterns were applied to the logarithm of the light intensity. The log-mean intensity of the broadband blue illumination was 0.1 W m^-2 and the standard deviation of the Gaussian white-noise was 0.58 decades. The results, in the form of temporal functions called Wiener kernels, represent the input-output relation of the light-growth response system. The transfer function, which was obtained as the Fourier transform of the first-order kernel, was analyzed in the frequency domain in terms of a dynamic model that consisted of a first-order high-pass filter, two secondorder low-pass filters, a delay element, and a gain factor. Parameters in the model (cutoff frequencies, damping coefficients, latency, and gain constant) were evaluated by nonlinear least-squares methods applied to the complex-valued transfer function. Analysis of the second-order kernel in the frequency domain suggests that the residual nonlinearity of the system lies close to the input.