Power Spectral Density Of Signal Research Articles

An automatic glucose monitoring signal denoising method with noise level estimation and responsive filter updating

Abstract Although continuous glucose monitoring (CGM) devices have been the crucial part of the artificial pancreas, their success has been discounted by random measurement noise. The difficulty of denoising methods for CGM is that the filter parameters are hard to be determined to well reflect the internal blood glucose dynamics and the real noise level. Besides, the noise level may change from device to device, subject to subject and also within the subject as time goes on which thus requires that the filter parameters should be adjusted to follow the noise changes. In this paper, we proposed an automatic CGM signal denoising method which covers three important components. First, the state transition matrix which reveals the internal blood glucose dynamics and plays an important role in determining filter parameters can be estimated in response to different patients. Second, the real noise level can be estimated which are used to set the values of filter parameters properly. Third, a responsive filter updating rule is developed which can judge whether the values of filter parameters should be updated in response to the variability of signal-to-noise ratio. The process of dealing with the CGM signals is executing as follows: the model parameters and the noise level are evaluated using Expectation Maximization (EM) algorithm which can fix proper filter parameters for the current signals. Then, a confidence interval is defined by computing the power spectral density (PSD) of the CGM signals to identify the changes of noise level which can tell whether or not the parameters of Kalman filter (KF) should be adjusted. The above issues are investigated based on thirty in silico subjects and ten clinical subjects. The proposed method can work well to identify the changes of noise level and determine proper filter parameters.

EEG sensorimotor rhythms' variation and functional connectivity measures during motor imagery: linear relations and classification approaches.

Hands motor imagery (MI) has been reported to alter synchronization patterns amongst neurons, yielding variations in the mu and beta bands’ power spectral density (PSD) of the electroencephalography (EEG) signal. These alterations have been used in the field of brain-computer interfaces (BCI), in an attempt to assign distinct MI tasks to commands of such a system. Recent studies have highlighted that information may be missing if knowledge about brain functional connectivity is not considered. In this work, we modeled the brain as a graph in which each EEG electrode represents a node. Our goal was to understand if there exists any linear correlation between variations in the synchronization patterns—that is, variations in the PSD of mu and beta bands—induced by MI and alterations in the corresponding functional networks. Moreover, we (1) explored the feasibility of using functional connectivity parameters as features for a classifier in the context of an MI-BCI; (2) investigated three different types of feature selection (FS) techniques; and (3) compared our approach to a more traditional method using the signal PSD as classifier inputs. Ten healthy subjects participated in this study. We observed significant correlations (p < 0.05) with values ranging from 0.4 to 0.9 between PSD variations and functional network alterations for some electrodes, prominently in the beta band. The PSD method performed better for data classification, with mean accuracies of (90 ± 8)% and (87 ± 7)% for the mu and beta band, respectively, versus (83 ± 8)% and (83 ± 7)% for the same bands for the graph method. Moreover, the number of features for the graph method was considerably larger. However, results for both methods were relatively close, and even overlapped when the uncertainties of the accuracy rates were considered. Further investigation regarding a careful exploration of other graph metrics may provide better alternatives.

On the Mechanisms Governing Spurious Tone Injection in Fractional PLLs

In fractional phase-locked loop driven by ${\Sigma \Delta }$ modulators there can be spurious tones in the power spectral density (PSD) of output signals even if the PSDs of the sequences used to drive the frequency divider are spur-free. This is due to undesirable nonlinear effects notably occurring in the charge pump (CP). In this brief, we focus on static and dynamic mismatch of the CP and its interaction with the digital delay usually present in the reset path of the phase-frequency detector. Despite the presence of nonlinearities, we show that spurs may not appear, and mechanisms governing their existence are unveiled. A compact and simple model is presented allowing the onset of spurs and their magnitude to be reliably estimated.

Can graph metrics be used for EEG-BCIs based on hand motor imagery?

Abstract The study of motor imagery (MI) has been a subject of great interest within the brain-computer interface (BCI) community. Several approaches have been proposed to solve the problem of classifying cerebral responses due to MI, mostly based on the power spectral density of the mu and beta bands; however, no optimum manner of proceeding through the fundamental steps of a MI-BCI has yet been established. In this work, we explored a relatively novel approach regarding feature generation for a MI-BCI by assuming that functional connectivity patterns of the brain are altered during hand MI. We modelled interactions among EEG electrodes by a graph, extracted metrics from it during left and right hand MI from eight subjects and classified the signals using commonly employed techniques in the BCI community (LDA and SVM). We also compared this approach to the more established method of using the signal power spectral density as the classifier features. With the graph method, we confirmed that only specific electrodes provide relevant information for data classification. A first approach provided maximum average classification rates across all subjects for the graph method of 86% for the mu band and 87% for the beta band. For the PSD method, average rates were of 98% and 99% for the mu and beta bands, respectively. However, a much larger number of features was needed: (130 ± 44) and (273 ± 89) for the mu and beta bands, respectively. Aiming to reproduce these rates using the graph method, pairwise inputs combinations of graph metrics were tested. They proved to be sufficient to obtain essentially the same classification accuracy rates, but with a considerably smaller number of features – about 60 features, for both bands. We thus conclude that the graph method is a feasible option for classification of hand MI signals.

Analytical Insights Into Parameter Estimation for Wiener Deconvolution

All real-time signals observed from various measurement systems require signal-processing techniques like the deconvolution, to compensate for the effect of transfer function of the systems. Wiener deconvolution is a widely used signal-processing technique for signal restoration. Often, if the power spectral density of signal and noise is unknown, the accuracy of the restored signal depends on an unknown filter parameter. In the literature, time-consuming, iterative, computational methods were reported to estimate the parameter. However, many of these methods give a range of optimum values instead of an unique value and often lead to either over-smoothing or under-smoothing. In this paper, novel analytical expressions are presented through which the unknown parameter can be estimated explicitly. The analytical results of this study are compared with the numerical methods, and they are found to be accurate and robust against numerical evaluation. Further, the results are demonstrated for signals obtained experimentally from the pulsed electroacoustic system and a network, in authors’ laboratory.

Brain waves-based index for workload estimation and mental effort engagement recognition

The advent of the communication systems and considering the complexity that some impose in their use, it is necessary to incorporate and equip these systems with a certain intelligence which takes into account the cognitive and mental capacities of the human operator. In this work, we address the issue of estimating the mental effort of an operator according to the cognitive tasks difficulty levels. Based on the Electroencephalogram (EEG) measurements, the proposed approach analyzes the user’s brain activity from different brain regions while performing cognitive tasks with several levels of difficulty. At a first time, we propose a variances comparison-based classifier (VCC) that makes use of the Power Spectral Density (PSD) of the EEG signal. The aim of using such a classifier is to highlight the brain regions that enter into interaction according to the cognitive task difficulty. In a second time, we present and describe a new EEG-based index for the estimation of mental efforts. The designed index is based on information recorded from two EEG channels. Results from the VCC demonstrate that powers of the Theta [4-7 Hz] (θ) and Alpha [8-12 Hz] (α) oscillations decrease while increasing the cognitive task difficulty. These decreases are mainly located in parietal and temporal brain regions. Based on the Kappa coefficients, decisions of the introduced index are compared to those obtained from an existing index. This performance assessment method revealed strong agreements. Hence the efficiency of the introduced index.

Fast convergent frequency-domain MIMO equalizer for few-mode fiber communication systems

Space division multiplexing using few-mode fibers has been extensively explored to sustain the continuous traffic growth. In few-mode fiber optical systems, both spatial and polarization modes are exploited to transmit parallel channels, thus increasing the overall capacity. However, signals on spatial channels inevitably suffer from the intrinsic inter-modal coupling and large accumulated differential mode group delay (DMGD), which causes spatial modes de-multiplex even harder. Many research articles have demonstrated that frequency domain adaptive multi-input multi-output (MIMO) equalizer can effectively compensate the DMGD and demultiplex the spatial channels with digital signal processing (DSP). However, the large accumulated DMGD usually requires a large number of training blocks for the initial convergence of adaptive MIMO equalizers, which will decrease the overall system efficiency and even degrade the equalizer performance in fast-changing optical channels. Least mean square (LMS) algorithm is always used in MIMO equalization to dynamically demultiplex the spatial signals. We have proposed to use signal power spectral density (PSD) dependent method and noise PSD directed method to improve the convergence speed of adaptive frequency domain LMS algorithm. We also proposed frequency domain recursive least square (RLS) algorithm to further increase the convergence speed of MIMO equalizer at cost of greater hardware complexity. In this paper, we will compare the hardware complexity and convergence speed of signal PSD dependent and noise power directed algorithms against the conventional frequency domain LMS algorithm. In our numerical study of a three-mode 112 Gbit/s PDM-QPSK optical system with 3000 km transmission, the noise PSD directed and signal PSD dependent methods could improve the convergence speed by 48.3% and 36.1% respectively, at cost of 17.2% and 10.7% higher hardware complexity. We will also compare the frequency domain RLS algorithm against conventional frequency domain LMS algorithm. Our numerical study shows that, in a three-mode 224 Gbit/s PDM-16-QAM system with 3000 km transmission, the RLS algorithm could improve the convergence speed by 53.7% over conventional frequency domain LMS algorithm.

Maximum-Likelihood Approach With Bayesian Refinement for Multichannel-Wiener Postfiltering

Multichannel signal enhancement is an important task, e.g., in modern speech communication. It can be approached in a mean-square error sense by multichannel Wiener filtering, which is often implemented as a cascade of spatial beamforming and spectral enhancement postfiltering. In this paper, we propose a novel Bayesian perspective on the problem of postfilter adaptation. Specifically, we present a two-step procedure for postfilter estimation. We first derive maximum-likelihood (ML) optimal estimators of the target signal and noise power spectral densities (PSD) employing the high-dimensional receiver data in conjunction with blindly estimated channels. When constructing a Wiener postfilter for noisy speech based on the respective speech and noise PSD estimates, this ML-based postfilter is capable of performing good speech enhancement, while leaving musical noise. Hence, we extend to a Bayesian estimation approach in a second step. By statistically modeling the ML-based postfilter estimation and further proposing a prior for the ideal Wiener postfilter, we derive a Bayesian refinement of the ML-based postfilter. This refinement then solely depends on the ML-based postfilter and is independent of the underlying high-dimensional data. Our Bayesian refinement is therefore implemented as a lightweight table look-up. Both proposed postfilters perform well in terms of segmental signal-to-noise ratio and perceptual evaluation of speech quality in various acoustical setups with nonstationary noise. The Bayes-refined postfilter offers consistent improvement over the ML-based postfilter and a single-channel speech enhancement baseline.

CE-OFDM Schemes: Spectral Characterization and Optimum Performance

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) techniques have been recently proposed to allow the use of power-efficient saturated amplifiers, since those signals do not have the high peak-to-average ratio of OFDM signals, but maintain most of the OFDM advantages. However, the nonlinear nature of the phase modulation process inherent to CE-OFDM schemes gives rise to both theoretical challenges (analytical difficulties due to the nonlinear processes involved) and practical challenges (spectral widening and possible performance degradation due to nonlinear distortion effects). In this work, we present accurate expressions for the average power spectral density of CE-OFDM signals. Making use of recent results that indicate performance gains associated to the optimum detection of nonlinearly distorted multicarrier signals, we also investigate the optimum detection of CE-OFDM signals considering both additive white Gaussian noise channels and frequency-selective channels with Rayleigh fading, providing theoretical expressions for the asymptotic gains as well as the correspondent approximate bit-error-rate results.

Differences Between Gait on Stairs and Flat Surfaces in Relation to Fall Risk and Future Falls.

We used body-worn inertial sensors to quantify differences in semi-free-living gait between stairs and on normal flat ground in older adults, and investigated the utility of assessing gait on these terrains for predicting the occurrence of multiple falls. Eighty-two community-dwelling older adults wore two inertial sensors, on the lower back and the right ankle, during several bouts of walking on flat surfaces and up and down stairs, in between rests and activities of daily living. Derived from the vertical acceleration at the lower back, step rate was calculated from the signal's fundamental frequency. Step rate variability was the width of this fundamental frequency peak from the signal's power spectral density. Movement vigor was calculated at both body locations from the signal variance. Partial Spearman correlations between gait parameters and physiological fall risk factors (components from the Physiological Profile Assessment) were calculated while controlling for age and gender. Overall, anteroposterior vigor at the lower back in stair descent was lower in subjects with longer reaction times. Older adults walked more slowly on stairs, but they were not significantly slower on flat surfaces. Using logistic regression, faster step rate in stair descent was associated with multiple prospective falls over 12 months. No significant associations were shown from gait parameters derived during walking upstairs or on flat surfaces. These results suggest that stair descent gait may provide more insight into fall risk than regular walking and stair ascent, and that further sensor-based investigation into unsupervised gait on different terrains would be valuable.

A new real-time signal processing approach for frequency-varying machinery

Development of condition monitoring approaches has played a key role in the stability and safety of frequency-varying machinery operations. Conventional time–frequency analysis methods suffer problems such as analysis results being too complex to realize highly intelligent and automated condition monitoring systems. Blind source separation is an attractive tool due to its excellent performance in separating defect source signals from their mixtures without detailed knowledge of sources and mixing processes; however, it can only be applied under some strict conditions. In this paper, a nonuniform sampling model is built and a new processing algorithm of frequency-varying signal is proposed. The relationship between the power spectral density (PSD) of the vibration signal of frequency-varying machinery and frequencies at different rotational speeds is derived. The proposed method can adaptively eliminate the influence of the varying rotational speed in the revised PSD. Some classical signal analysis methods are implemented to compare with the proposed approach by simulations. An experiment has been conducted by using a JD-1 wheel/rail simulation facility to illustrate the effectiveness of the proposed method.

Optical feedback in dfb quantum cascade laser for mid-infrared cavity ring-down spectroscopy

A simple external optical feedback system has been applied to a distributed feedback quantum cascade laser (DFB QCL) for cavity ring-down spectroscopy (CRDS) and a clear effect of feedback was observed. A long external feedback path length of up to 4m can decrease the QCL linewidth to around 50kHz, which is of the order of the transmission linewidth of our high finesse ring-down cavity. The power spectral density of the transmission signal from high finesse cavity reveals that the noise at frequencies above 20kHz is reduced dramatically.

Demonstration of NLFM Waveforms With Experiments and Doppler Shift Compensation for SAR Application

Range sidelobe suppression in synthetic aperture radars (SARs) is conventionally realized using amplitude weighting with windowing functions in either time or frequency domains, which would result in a reduced signal-to-noise ratio (SNR) of the output. To counterbalance the loss, a system with more complexity and cost is needed, especially for spaceborne SAR. Fortunately, nonlinear frequency modulation (NLFM) chirp waveforms, which can shape the signal's power spectral density and offer radar matched filter output with lower sidelobes at no cost of reduced SNR, is a promising candidate. In this letter, the proof-of-principle experiment is presented to construct NLFM transmitting pulses using a real SAR system platform on the ground and analyze the characteristics of the pulses. Two approaches are developed to perform system-specific predistortion and the advantage of NLFM waveforms with better SNR is demonstrated using the theoretical derivation and experimental results. For spaceborne NLFM SAR, the effect of Doppler shift on NLFM SAR imaging cannot be neglected. Therefore, for further promoting the application of NLFM in SAR, one effective compensation approach is developed. All the experimental results and analysis validate the promising potential of NLFM for SAR application.

Correlation and spectral properties of chaotic signals generated by a piecewise-linear map with multiple segments

In recent decades, many studies with practical applications of chaotic signals in telecommunications and signal processing have been carried out. Although spectral analysis is of relevance in these areas, there are few analytical results concerning the spectral characterization of chaotic signals. In this work, we deduce analytical expressions for autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by a piecewise-linear map, with multiple segments. We present numerical simulations to confirm the theoretical results.

High-Order UWB Pulses Generation Adaptable to Bi-Phase Modulation

In this letter, we present a high-order impulse-radio ultra-wideband (UWB) pulses generator based on the processing of incoherent optical signals by a dispersive element. The full waveform reconfigurability is achieved by the control of the optical signal power spectral density profile. Operation principle is experimentally shown by the generation of classical UWB pulses: monocycle and doublet. High-order UWB pulses generation is experimentally demonstrated by the generation of triplet and quadruplet. Also, the proper adjustment of the optical signal power distribution permits to reduce the baseband content of the synthesized waveform, which is critical in UWB environments to achieve spectrally efficient solutions. Moreover, system flexibility allows the adaptation to a bi-phase modulation scheme. This feature has been proved by the generation of the inverted version of the UWB pulses achieved in this letter.

Functional brain networks in healthy subjects under acupuncture stimulation: An EEG study based on nonlinear synchronization likelihood analysis

Electroencephalogram (EEG) signal evoked by acupuncture stimulation at ”Zusanli” acupoint is analyzed to investigate the modulatory effect of manual acupuncture on the functional brain activity. Power spectral density of EEG signal is first calculated based on the autoregressive Burg method. It is shown that the EEG power is significantly increased during and after acupuncture in delta and theta bands, but decreased in alpha band. Furthermore, synchronization likelihood is used to estimate the nonlinear correlation between each pairwise EEG signals. By applying a threshold to resulting synchronization matrices, functional networks for each band are reconstructed and further quantitatively analyzed to study the impact of acupuncture on network structure. Graph theoretical analysis demonstrates that the functional connectivity of the brain undergoes obvious change under different conditions: pre-acupuncture, acupuncture, and post-acupuncture. The minimum path length is largely decreased and the clustering coefficient keeps increasing during and after acupuncture in delta and theta bands. It is indicated that acupuncture can significantly modulate the functional activity of the brain, and facilitate the information transmission within different brain areas. The obtained results may facilitate our understanding of the long-lasting effect of acupuncture on the brain function.

Theoretical Analysis of the Power Spectral Density for FFT-FBMC Signals

Filter-bank multicarrier (FBMC) modulation is appreciated for its spectrum well-localization. However, the drawback of FBMC is the presence of the intrinsic interference that prevents the application of some multiple input multiple output techniques. Recently, fast Fourier transfrom (FFT)-FBMC was proposed to get rid of the intrinsic interference by performing FFT/IFFT (i.e., inverse fast Fourier transform) precoding and postcoding on each subcarrier. Consequently, FFT-FBMC affects and modifies the spectrum of the transmitted signal. In this letter, we address the power spectral density (PSD) of the FFT-FBMC transmitted signal. We theoretically derive the expression of the PSD of FFT-FBMC signal. We also show that the FFT precoding of the signals on each subcarrier has the advantage to reduce the frequency band occupied by each subcarrier. Consequently, we will show that FFT-FBMC spectrum is more frequency-localized than that of the conventional FBMC.

An unsupervised subject identification technique using EEG signals.

In this work, EEG spectral features of different subjects are uniquely mapped into a 2D feature space. Such distinctive 2D features pave the way to identify subjects from their EEG spectral characteristics in an unsupervised manner without any prior knowledge. First, we extract power spectral density of EEG signals in different frequency bands. Next, we use t-distributed stochastic neighbor embedding to map data points from high dimensional space in a visible 2D space. Such non-linear data embedding method visualizes different subjects' data points as well-separated islands in two dimensions. We use a fuzzy c-means clustering technique to identify different subjects without any prior knowledge. The experimental results show that our proposed method efficiently (precision greater than 90%) discriminates 10 subjects using only the spectral information within their EEG signals.

Vortex-induced vibration of a tube array with a large pitch-to-diameter ratio value

To study the vortex-induced vibration behaviors of tube arrays with large pitch-to-diameter ratio values, an experiment has been conducted by testing the responses of an elastically mounted tube in a fixed normal triangular tube array with five rows and a pitch-to-diameter ratio value of 2.5 in a water tunnel subjected to cross-flow. The amplitude curves, power spectral density, and response frequencies were obtained in both in-line and transverse directions through the experiment. The results show that the responses obtained from the in-line direction are quite different from those obtained from the transverse direction. In the in-line vibration, there were two excitation regions, yet in the transverse vibration, there was only one excitation region. Moreover, in the in-line vibration, two obvious prominent peaks can be observed in the power spectral density of the vibration signal. The second prominent peak is a subharmonic peak. The frequency corresponding to the subharmonic peak was nearly twice as high as that corresponding to the first peak. However, in the transverse vibration, only a single broad peak existed in the power spectral density of the vibration signal. The hysteresis and the “lock-in” phenomena appeared in both the in-line and transverse vibrations. The results of study are beneficial for designing and operating devices mounted with large pitch-to-diameter ratio tube arrays, and for further research on the vortex-induced vibration of tube arrays.

Comparison of in-Flight Measured and Computed Aeroelastic Damping: Modal Identification Procedures and Modeling Approaches

The Operational Modal Analysis technique is a methodology very often applied for the identification of dynamic systems when the input signal is unknown. The applied methodology is based on a technique to estimate the Frequency Response Functions and extract the modal parameters using only the structural dynamic response data, without assuming the knowledge of the excitation forces. Such approach is an adequate way for measuring the aircraft aeroelastic response due to random input, like atmospheric turbulence. The in-flight structural response has been measured by accelerometers distributed along the aircraft wings, fuselage and empennages. The Enhanced Frequency Domain Decomposition technique was chosen to identify the airframe dynamic parameters. This technique is based on the hypothesis that the system is randomly excited with a broadband spectrum with almost constant power spectral density. The system identification procedure is based on the Single Value Decomposition of the power spectral densities of system output signals, estimated by the usual Fast Fourier Transform method. This procedure has been applied to different flight conditions to evaluate the modal parameters and the aeroelastic stability trends of the airframe under investigation. The experimental results obtained by this methodology were compared with the predicted results supplied by aeroelastic numerical models in order to check the consistency of the proposed output-only methodology. The objective of this paper is to compare in-flight measured aeroelastic damping against the corresponding parameters computed from numerical aeroelastic models. Different aerodynamic modeling approaches should be investigated such as the use of source panel body models, cruciform and flat plate projection. As a result of this investigation it is expected the choice of the better aeroelastic modeling and Operational Modal Analysis techniques to be included in a standard aeroelastic certification process.