Number Of Zero-crossings Research Articles

Association between movement speed and instability catch kinematics and the differences between individuals with and without chronic low back pain

Studies reported the existence of instability catch (IC) during trunk flexion in patients with chronic low back pain (CLBP). However, different movement speeds can cause different neuromuscular demands resulting in altered kinematic patterns. In addition, kinematic characterization corresponding to clinical observation of IC is still limited. Therefore, this study aimed to determine (1) the association between movement speed and kinematic parameters representing IC during trunk flexion and (2) the differences in kinematic parameters between individuals with and without CLBP. Fifteen no low back pain (NoLBP) and 15 CLBP individuals were recruited. Inertial measurement units (IMU) were attached to T3, L1, and S2 spinous processes. Participants performed active trunk flexion while IMU data were simultaneously collected. Total trunk, lumbar, and pelvic mean angular velocity (T_MV, L_MV, and P_MV), as well as number of zero-crossings, peak-to-peak, and area of sudden deceleration and acceleration (Num, P2P, and Area), were derived. Pearson’s correlation tests were used to determine the association between T_MV and L_MV, P_MV, Num, P2P, and Area. An ANCOVA was performed to determine the difference in kinematic parameters between groups using movement speed as a covariate. Significant associations (P < 0.05) were found between movement speed and other kinematic parameters, except for Area. Results showed that L_MV significantly differed from the P_MV (P = 0.002) in the CLBP group, while a significant between-group difference (P = 0.037) was found in the P_MV. Additionally, significant between-group differences (P < 0.05) in P2P and Area were observed. The associations between movement speed and kinematic parameters suggest that movement speed changes can alter kinematic patterns. Therefore, clinicians may challenge lumbopelvic neuromuscular control by modifying movement speed to elicit greater change in kinematic patterns. In addition, the NoLBP group used shared lumbar and pelvic contributions, while the CLBP group used less pelvic contribution. Finally, P2P and Area appeared to offer the greatest sensitivity to differentiate between the groups. Overall, these findings may enhance the understanding of the mechanism underlying IC in CLBP.

Comparison of Various Smoothness Metrics for Upper Limb Movements in Middle-Aged Healthy Subjects.

Metrics for movement smoothness include the number of zero-crossings on the acceleration profile (N0C), the log dimensionless jerk (LDLJ), the normalized averaged rectified jerk (NARJ) and the spectral arc length (SPARC). Sensitivity to the handedness and movement type of these four metrics was compared and correlations with other kinematic parameters were explored in healthy subjects. Thirty-two healthy participants underwent 3D upper limb motion analysis during two sets of pointing movements on each side. They performed forward- and backward-pointing movements at a self-selected speed to a target located ahead at shoulder height and at 90% arm length, with and without a three-second pause between forward and backward movements. Kinematics were collected, and smoothness metrics were computed. LDLJ, NARJ and N0C found backward movements to be smoother, while SPARC found the opposite. Inter- and intra-subject coefficients of variation were lowest for SPARC. LDLJ, NARJ and N0C were correlated with each other and with movement time, unlike SPARC. There are major differences between smoothness metrics measured in the temporal domain (N0C, LDLJ, NARJ), which depend on movement time, and those measured in the frequency domain, the SPARC, which gave results opposite to the other metrics when comparing backward and forward movements.

Age-Related Change of Head Control in Response to Postural Perturbations

<h3>Research Objectives</h3> To explore if older adults, particularly those over 75 years, have more zero-crossings to restore head stabilization than young adults after postural perturbations. <h3>Design</h3> Cross-sectional study. <h3>Setting</h3> Laboratory setting. <h3>Participants</h3> A convenient sample of 57 healthy participants without a current or past history of neck-related dysfunction, trauma, deformities, and uncontrolled balance issues were recruited. They were grouped by age: Young (18-30 yrs, age: 22.3±3.8), Young-Old (60-74 yrs, age: 67.2±3.8), and Old-Old (>75+ yrs, age: 81.1±5.3). <h3>Interventions</h3> Not applicable. <h3>Main Outcome Measures</h3> Accelerometers (Delsys) were attached on the forehead and C7 of participants as they experienced the unexpected platform translations (Neurocom). A total of six trials were performed in random order including three anterior and posterior perturbations. The linear head acceleration in the vertical, anteroposterior, and mediolateral axis were extracted. A custom Matlab code computed the resultant head acceleration, detected the head re-stabilization time of each trail, and determined the number of zero-crossings during the head re-stabilization of three axes. <h3>Results</h3> Significant less zero-crossings in the Young group were noted in the vertical (p = 0.011, η2 = 0.07) and AP (p = 0.030, η2 = 0.05) axes of posterior platform translation. Despite no statistical differences found in other conditions, a trend of increased zero-crossing with aging was suggested. The Old-Old group consistently showed the greatest number of zero-crossings across all the conditions. <h3>Conclusions</h3> Older adults appear to recruit a different head stabilization strategy in response to postural perturbations. The oldest age group (over 75 years) seems to show more vigorous neuromuscular control to restore the postural stabilization in the head-neck segment after the perturbation than the younger counterparts. <h3>Author(s) Disclosures</h3> Authors declared that none of us had relevant or material financial interests that relate to the research described in this research project.

Structural fatigue reliability evaluation based on probability analysis of the number of zero-crossings of stochastic response process

Structural fatigue failure is closely related to the number of stress cycles. Therefore, the number of the intersections between stochastic response process and zero-boundary is a key problem in structural fatigue reliability analysis. In this paper, the relationship between the number of the multiple intersections and the fatigue cumulative damage index is derived according to the Miner rule-based high cycle fatigue random cumulative damage index. Then, use random walk to approximately simulate Wiener process, and get the first intersection probability between Wiener process and the zero-boundary. Next, further utilize the renewal process to solve the distribution law of the number of intersections between the Wiener process and the zero-boundary in a period of time. Finally, based on the fatigue failure criterion considering the randomness of the failure threshold, the calculation formula the structural fatigue reliability is derived. As a practical example, the fatigue reliabilities of the key part of Metro Bogie under different operation periods are analyzed using the proposed method.

Assessing Walking Stability Based on Whole-Body Movement Derived from a Depth-Sensing Camera.

Stability during walking is considered a crucial aspect of assessing gait ability. The current study aimed to assess walking stability by applying principal component analysis (PCA) to decompose three-dimensional (3D) whole-body kinematic data of 104 healthy young adults (21.9 ± 3.5 years, 54 females) derived from a depth-sensing camera into a set of movement components/synergies called “principal movements” (PMs), forming together to achieve the task goal. The effect of sex as the focus area was tested on three PCA-based variables computed for each PM: the relative explained variance (rVAR) as a measure of the composition of movement structures; the largest Lyapunov exponent (LyE) as a measure of variability; and the number of zero-crossings (N) as a measure of the tightness of neuromuscular control. The results show that the sex effects appear in the specific PMs. Specifically, in PM1, resembling the swing-phase movement, females have greater LyE (p = 0.013) and N (p = 0.017) values than males. Moreover, in PM3, representing the mid-stance-phase movement, females have smaller rVAR (p = 0.020) but greater N (p = 0.008) values than males. These empirical findings suggest that the inherent sex differences in walking stability should be considered in assessing and training locomotion.

A Novel Hybrid Approach for the Identification of Clear Air and Rain Echoes in the 205 MHz ST Radar Spectrum

Stratosphere–troposphere (ST) wind profiler radar (WPR) installed at Cochin, India, is a clear air VHF Doppler radar system designed for continuous wind velocity measurements under all-weather conditions. Clear air WPRs detect backscattered signals due to Bragg scattering from small irregularities in the refractive index caused by turbulence. The 205-MHz frequency band is able to detect both clear air and rain echos, simultaneously. Due to the large spectral width and merging of clear and rain echoes during rainy periods, the conventional signal processing techniques become inept at distinguishing the two echoes. An innovative hybrid approach is applied in this study to mitigate the ambiguity in identifying clear air and rain echoes separately. A combination of an exponentially modified Gaussian model and a pure Gaussian model is used to fit the raw spectrum in the hybrid approach adaptively. The data adaptive fitting procedure adopted can identify two distinct peaks during the rainy period, and the fitting process reduces to a single peak during non-rainy periods. Furthermore, the number of peaks is confirmed by locating the number of zero-crossings (NZCs) of the power gradient of the fit data. This unique approach is applied in the 205-MHz ST radar framework for the first time to solve the issue of multiple peaking in the ST radar spectrum.

Online Identification of Underlying Causes for Multiple and Multi-Stage Power Quality Disturbances Using S-Transform

ABSTRACT The proposed methodology aims at the identification of multiple and multi-stage power quality (PQ) disturbances along with their underlying causes. To this end, a computationally efficient S-Transform with decision tree (DT) based online PQ monitoring algorithm has been presented in this paper. This online algorithm provides a sample-based analysis of 40-dB noisy multiple and multi-stage PQ disturbance signals simulated in MATLAB environment with the different combinations of underlying causes as per the IEEE-1159 standard. The features like residual voltage, instantaneous phase-angle jump (IPAJ), and number of zero crossings (NZC) have been extracted from the transformed contours, viz., maximum voltage amplitude versus time (MVAVT) and phase-angle versus time (PAVT). Henceforth, the accurate recognition of most common underlying causes like three-phase fault, induction motor starting, and capacitor bank energizing has been achieved. For the first time, an online PQ monitoring algorithm is effectively assessing the type and underlying cause of a multiple or multi-stage disturbance simultaneously. The proposed methodology has also been experimentally validated with real-time PQ disturbance signals acquired in the laboratory.

Human Gait Recognition Based on Multiple Feature Combination and Parameter Optimization Algorithms.

Accuracy is a key index of human gait recognition. In this paper, we propose an improved gait recognition algorithm, which combines multiple feature combination and artificial bee colony for optimizing the support vector machine (ABC-SVM). Firstly, considering the complexity characteristics of surface electromyography (sEMG) signals, four types of features are extracted from the denoised sEMG signals, including the time-domain features of integral of absolute value (IAV), variance (VAR), and number of zero-crossing (ZC) points, frequency-domain features of mean power frequency (MPF) and median frequency (MF), and wavelet features and fuzzy entropy features. Secondly, the classifiers of SVM, linear discriminant analysis (LDA), and extreme learning machine (ELM) are employed to recognize the gait with obtained features, including singe-class features, multiple combination features, and optimized features of dimension reduction by principal component analysis (PCA). Thirdly, the penalty coefficient and kernel function parameter of the SVM classifier are optimized by the ABC algorithm, and the influence of different features and classifiers on the recognition results is studied. Finally, the feature samples selected to construct the SVM classifier are trained and recognized. Results show that the classification performance of the ABC-SVM classifier is significantly better than that of the nonoptimized SVM classifier, and the average recognition rate is increased by 3.18%. In addition, the combined feature samples (time-domain, frequency-domain, wavelet, and fuzzy entropy features) not only improve the gait classification accuracy but also enhance the recognition stability.

Evaluation of time domain features on detection of epileptic seizure from EEG signals

In the study of detection of an epileptic seizure using Electroencephalogram (EEG), pattern recognition has been recognised as a valued tool. In this pattern recognition study, the first time the authors have attempted to use time domain (TD) features such as waveform length (WL), number of zero-crossings (ZC) and number of slope sign changes (SSC) derived directly from filtered EEG data and from discrete wavelet transform (DWT) of filtered EEG data for the detection of an epileptic seizure. Further, the authors attempted to study the performance of other time domain features such as mean absolute value (MAV), standard deviation (SD), average power (AVP) which had been attempted by other researchers. The performance of the TD features is studied using naive Bayes (NB) and support vector machines (SVM) classifiers for University of Bonn database with fourteen different combinations of set E with set A to D and clinically inferred with Christian Medical College, Vellore database. The proposed scheme was also compared with other existing scheme in the literature. The implementation results showed that the proposed scheme could attain the highest accuracy of 100% for normal eyes open and epileptic data set with direct as well as DWT based TD features. For other data sets, the highest accuracy are obtained with DWT based TD features using SVM.

Reconfigurable optical generation of nine Nyquist WDM channels with sinc-shaped temporal pulse trains using a single microresonator-based Kerr frequency comb.

Sinc-shaped temporal pulse trains have a spectrally efficient, rectangular Nyquist spectrum. We demonstrate the simultaneous and reconfigurable optical generation of multiple Nyquist-shaped wavelength-division-multiplexed (WDM) channels having temporal sinc-shaped pulse trains as data carriers. The channels are generated through the insertion of coherent lines using cascaded continuous-wave amplitude modulation around the spectral lines of a microresonator-based Kerr optical frequency comb. For each of nine Kerr frequency comb lines, we insert sub-groups of uniform and coherent lines to generate nine WDM channels. The deviations from ideal Nyquist pulses for the nine channels at repetition rates of 6 and 2GHz are between 4.2%-6.1% and 2%-4.5%, respectively. Each WDM channel is modulated with on-off keying (OOK) at 6 Gbit/s. In addition, we show the reconfigurability of this method by varying the number of WDM channels, the generated sinc-shaped pulse train repetition rates, the duration, and the number of zero-crossings.

Diagnosis of traditional Chinese medicine constitution by integrating indices of tongue, acoustic sound, and pulse

IntroductionInspection, auscultation, and pulse-taking are the three physical examinations used by traditional Chinese medicine (TCM) practitioners to diagnose constitution. The aim of this study was to integrate biological signals extracted from these three examinations, including tongue image, waves of acoustic sound, and pulse waveforms, into the same model in order to identify TCM constitutions. MethodsTongue images, acoustic sound, and pulse waveforms were abstracted from 274 subjects, and indices of biological signals were extracted. Constitution scores were measured using the Nine-Constitution Scale questionnaire. Association between indices and constitution scores were analyzed by Pearson correlation analysis. For each of the eight abnormal constitutions, indices significantly correlated to the abnormal constitution were further used as arguments in a linear regression model to build an equation for predicting the constitution score. ResultsTongue indices that were identified to be associated with abnormal constitutions included the G, B, S and b color values, maximum width of tongue body, number of red spots on the tongue surface, and proportion of scalloped tongue margin. Acoustic sound indices included intensity, average number of zero-crossing, high spectral energy ratio, and pitch of the acoustic sound. Pulse waveform indices included the height of the main wave, unsmooth wave, single systolic area, and rapid ejection time. ConclusionsThis study identified indices that are associated with scores of abnormal constitutions. Indices having a larger correlation coefficient can be considered to have larger relative weight in determination of the corresponding constitution. The equations make it possible to predict constitution scores based on biological signals of the tongue, acoustic sound, and pulse.

Evaluation of time domain features using best feature subsets based on mutual information for detecting epilepsy

In this pattern recognition study of detecting epilepsy, the first time the authors have attempted to use time domain (TD) features such as waveform length (WL), number of zero-crossings (ZC) and number of slope sign changes (SSC) which are extracted from the discrete wavelet transform (DWT) for the detecting the epilepsy for University of Bonn datasets and real-time clinical data. The performance of these TD features is studied along with mean absolute value (MAV) which has been attempted by other researchers. The performance of the TD features derived from DWT is studied using naive Bayes (NB) and support vector machines (SVM) for five different datasets from University of Bonn with 14 different combinations datasets and 24 patients datasets from Christian Medical College and Hospital (CMCH), India database. Using feature selection and feature ranking based on the estimation of mutual information (MI), the significant features required for the classifier to get higher accuracy is obtained. Further, NB achieves 100% classification accuracy (CA) in distinguishing normal eyes open and epileptic dataset with top 4 ranked features and it gives 100% accuracy with top-ranked two features in using CMCH data.

Effect of filtering with time domain features for the detection of epileptic seizure from EEG signals

Pattern recognition plays an important role in the detection of epileptic seizure from electroencephalogram (EEG) signals. In this pattern recognition study, the effect of filtering with the time domain (TD) features in the detection of epileptic signal has been studied using naive Bayes (NB) and supports vector machines (SVM). It is the first time the authors attempted to use TD features such as waveform length (WL), number of zero-crossings (ZC) and number of slope sign changes (SSC) derived from the filtered and unfiltered EEG data, and performance of these features is studied along with mean absolute value (MAV) which has been already attempted by the researchers. The other TD features which are attempted by the researchers such as standard deviation (SD) and average power (AVP) along with MAV are studied. A comparison is made in effect of filtering and without filtering for the University of Bonn database using NB and SVM for the TD features attempted first time along with MAV. The effect of individual and combined TD features is studied and the highest classification accuracy obtained in using direct TD features would be 99.87%, whereas it is 100% with filtered EEG data. The raw EEG data can be segmented and filtered using the fourth-order Butterworth band-pass filter.

Pattern of improvement in upper limb pointing task kinematics after a 3-month training program with robotic assistance in stroke

BackgroundWhen exploring changes in upper limb kinematics and motor impairment associated with motor recovery in subacute post stroke during intensive therapies involving robot-assisted training, it is not known whether trained joints improve before non-trained joints and whether target reaching capacity improves before movement accuracy.MethodsTwenty-two subacute stroke patients (mean delay post-stroke at program onset 63 ± 29 days, M2) underwent 50 ± 17 (mean ± SD) 45-min sessions of robot-assisted (InMotion™) shoulder/elbow training over 3 months, in addition to conventional occupational therapy. Monthly evaluations (M2 to M5) included Fugl-Meyer Assessment (FM), with subscores per joint, and four robot-based kinematic measures: mean target distance covered, mean velocity, direction accuracy (inverse of root mean square error from straight line) and movement smoothness (inverse of mean number of zero-crossings in the velocity profile). We assessed delays to reach statistically significant improvement for each outcome measure.ResultsAt M5, all clinical and kinematic parameters had markedly improved: Fugl-Meyer, +65% (median); distance covered, +87%; mean velocity, +101%; accuracy, +134%; and smoothness, +96%. Delays to reach statistical significance were M3 for the shoulder/elbow Fugl-Meyer subscore (+43%), M4 for the hand (+80%) and M5 for the wrist (+133%) subscores. For kinematic parameters, delays to significant improvements were M3 for distance (+68%), velocity (+65%) and smoothness (+50%), and M5 for accuracy (+134%).ConclusionsAn intensive rehabilitation program combining robot-assisted shoulder/elbow training and conventional occupational therapy was associated with improvement in shoulder and elbow movements first, which suggests focal behavior-related brain plasticity. Findings also suggested that recovery of movement quantity related parameters (range of motion, velocity and smoothness) might precede that of movement quality (accuracy).Trial registrationEudraCT 2016–005121-36. Date of Registration: 2016–12-20. Date of enrolment of the first participant to the trial: 2009–11-24 (retrospective data).

Automated ECG Noise Detection and Classification System for Unsupervised Healthcare Monitoring.

Automatic detection and classification of noises can play a vital role in the development of robust unsupervised electrocardiogram (ECG) analysis systems. This paper proposes a novel unified framework for automatic detection, localization, and classification of single and combined ECG noises. The proposed framework consists of the modified ensemble empirical mode decomposition (CEEMD), the short-term temporal feature extraction, and the decision-rule-based noise detection and classification. In the proposed framework, ECG signals are first decomposed using the modified CEEMD algorithm for discriminating the ECG components from the noises and artifacts. Then, the short-term temporal features such as maximum absolute amplitude, number of zerocrossings, and local maximum peak amplitude of the autocorelation function are computed from the extracted high-frequency and low-frequency signals. Finally, a decision rule-based algorithm is presented for detecting the presence of noises and classifying the processed ECG signals into six signal groups: noise-free ECG, ECG+BW, ECG+MA, ECG+PLI, ECG+BW+PLI, and ECG+BW+MA. The proposed framework is rigorously evaluated on five benchmark ECG databases and the real-time ECG signals. The proposed framework achieves an average sensitivity of 99.12%, specificity of 98.56%, and overall accuracy of 98.90% in detecting the presence of noises. Classification results show that the framework achieves an average sensitivity, positive predictivity, and classification accuracy of 98.93%, 98.39%, and 97.38%, respectively. The proposed framework not only achieves better noise detection and classification rates than the current state-of-the-art methods but also accurately localizes short bursts of noises with low endpoint delineation errors. Extensive studies on benchmark databases demonstrate that the proposed framework is more suitable for reducing false alarm rates and selecting appropriate noise-specific denoising techniques in automated ECG analysis applications.

Bulk spectroscopic measurement of the topological charge of Weyl nodes with resonant x rays

We formulate a bulk spectroscopic method for direct measurement of the topological invariant of nondegenerate band crossings in Weyl semimetals. We demonstrate how polarization-resolved resonant x-ray scattering captures the winding of the Berry flux around Weyl nodes. The spectra obtained by the proposed strategy feature an integer number of zero-crossings that is directly related to the topological charge of the measured nodes. We benchmark the proposed protocol on TaAs, using realistic low-energy models derived from density-functional theory to accurately represent the states close to the Fermi level, including sizable deviations from the idealized linear dispersion. We conclude that the proposed measurement, which is within the reach of current experimental setups, yields direct signatures of nontrivial band topology in spectroscopy of three-dimensional bulk matter.

Concurrent validity and test-retest reliability of the Virtual Peg Insertion Test to quantify upper limb function in patients with chronic stroke.

BackgroundMeasuring arm and hand function of the affected side is vital in stroke rehabilitation. Therefore, the Virtual Peg Insertion Test (VPIT), an assessment combining virtual reality and haptic feedback during a goal-oriented task derived from the Nine Hole Peg Test (NHPT), was developed. This study aimed to evaluate (1) the concurrent validity of key outcome measures of the VPIT, namely the execution time and the number of dropped pegs, with the NHPT and Box and Block Test (BBT), and (2) the test-retest-reliability of these parameters together with the VPIT’s additional kinetic and kinematic parameters in patients with chronic stroke.The three tests were administered on 31 chronic patients with stroke in one session (concurrent validity), and the VPIT was retested in a second session 3–7 days later (test-retest reliability). Spearman rank correlation coefficients (ρ) were calculated for assessing concurrent validity, and intraclass correlation coefficients (ICCs) were used to determine relative reliability. Bland-Altman plots were drawn and the smallest detectable difference (SDD) was calculated to examine absolute reliability.ResultsFor the 31 included patients, 11 were able to perform the VPIT solely via use of their affected arm, whereas 20 patients also had to utilize support from their unaffected arm. For n = 31, the VPIT showed low correlations with the NHPT (ρ = 0.31 for time (Tex[s]); ρ = 0.21 for number of dropped pegs (Ndp)) and BBT (ρ = −0.23 for number of transported cubes (Ntc); ρ = −0.12 for number of dropped cubes (Ndc)). The test-retest reliability for the parameters Tex[s], mean grasping force (Fggo[N]), number of zero-crossings (Nzc[1/sgo/return) and mean collision force (Fcmean[N]) were good to high, with ICCs ranging from 0.83 to 0.94. Fair reliability could be found for Fgreturn (ICC = 0.75) and trajectory error (Etrajgo[cm]) (0.70). Poor reliability was measured for Etrajreturn[cm] (0.67) and Ndp (0.58). The SDDs were: Tex = 70.2 s, Ndp = 0.4 pegs; Fggo/return = 3.5/1.2 Newton; Nzc[1/s]go/return = 0.2/1.8 zero-crossings; Etrajgo/return = 0.5/0.8 cm; Fcmean = 0.7 Newton.ConclusionsThe VPIT is a promising upper limb function assessment for patients with stroke requiring other components of upper limb motor performance than the NHPT and BBT. The high intra-subject variation indicated that it is a demanding test for this stroke sample, which necessitates a thorough introduction to this assessment. Once familiar, the VPIT provides more objective and comprehensive measurements of upper limb function than conventional, non-computerized hand assessments.

Incoherent Undersampling-Based Waveform Reconstruction Using a Time-Domain Zero-Crossing Metric

Incoherent undersampling-based waveform acquisition provides a low-cost test setup for characterizing high-speed systems. A periodic waveform reconstruction using incoherent undersampling remaps time indices of samples using the modulus of the suspected period of the signal, effectively folding the signal into a time window equal to one period. The major cost and accuracy limitations of the reconstruction technique arise from estimation of the waveform period. Multiple cost functions have been proposed to estimate the period, including frequency domain metrics, which are computationally intensive. In this paper, we propose a new time domain zero-crossing (ZC)-based metric, where the metric gives the number of ZC in the reconstructed waveform for an assumed period of the waveform. The reconstruction technique is also extended to beyond the track-and-hold amplifier bandwidth using a novel test setup combining the incoherent undersampling with multichannel bandwidth interleaving.

Method for Evaluating Periodic Trends in Measured Signals Based on the Number of Zero Crossings

A method is proposed for evaluating the frequency of periodic trends based on the number of zero crossings by a signal. This method is distinguished by low computation time requirements. Test results demonstrate the possible use of this method in practical applications.

&lt;formula formulatype="inline"&gt;&lt;tex Notation="TeX"&gt;$\epsilon$&lt;/tex&gt; &lt;/formula&gt;-Mono-Component: Its Characterization and Construction

This paper studies the consistency between the analytic amplitude and the physical amplitude for a mono-component of the form s(t)=ρ(t)e iθ(t) . A special class of mono-components, called e-mono-components, are considered and a parameter e is introduced to measure the consistency between these two kinds of amplitudes. It is shown that e controls the number of zerocrossings of s(t) within each monotonic interval of ρ(t), which means that the oscillation of the analytic amplitude ρ(t) is much slower than that of the phase part e iθ(t) at any instant, provided that e is sufficiently small. Some sufficient conditions, including the Fourier spectral characterization, for s(t)=ρ(t)e iθ(t) to be an e-mono-component are given. Frames and Riesz bases composed of e-mono-components are constructed. Finally, applications of e-mono-components to signal decomposition and time-frequency analysis are discussed.