Discrete Signals Research Articles

Input-and-Measurement Event-Triggered Output-Feedback Chattering Reduction Control for MEMS Gyroscopes

This article presents an input-and-measurement event-triggered output-feedback chattering reduction control for microelectromechanical system (MEMS) gyroscopes. To realize online estimation with decreased communication burden along sensor-to-control channel, a switching threshold-based sampler is embedded to achieve an intermittent measurement-based extended state observer (IMESO) capable of synchronously observing unavailable velocity states and disturbances, meanwhile, a mathematical presentation reflecting the interaction between design parameters and upper boundary of estimation errors is deduced to make argument tuning easy. Next, an event-triggered output-feedback control rule is developed in the controller-to-actuator channel to obtain a discrete control signal with less occupation on communication resources without inducing Zeno phenomena. Besides, to enforce system profiles evolve within the predefined performance boundaries with reduced chattering, a tracking differentiator (TD)-based prescribed performance control (TDPPC) is proposed, where the time differentiation of the preselected envelopes can be managed with smooth transient, and a balance between system performance and sampling cost can be ensured. Finally, a sigmoid function-based TD (STD), rather than dynamic surface control, is utilized to overcome the complexity explosion. Comparison simulations are performed to show the superiorities and effectiveness of the established controller.

Identifying influential observations in a time series from the frequency domain point of view

This study attempts to explore the influence of observations in a time series or a discrete time signal. The goal is to detect abnormal observations from a frequency domain point of view, while the most of relevant studies have been done from a time domain point of view. The concept of the influence function in the field of robust statistics is borrowed to identify influential observations in a time series. An empirical version of the influence function on the discrete Fourier transform of a time series is designed and subsequently a statistic is proposed to identify influential observations of a time series from the frequency domain point of view. Though the proposed statistic is simple enough to be calculated with simple arithmetic operations, case studies show that the proposed method is capable of identifying influential or abnormal observations of a time series. By identifying influential or abnormal observations, we would be able to gain a better understanding of the nature of a time series and to control possible future influential observations.

Optimal ternary sequence sets rigorously achieving the Welch bound

Sequences are finite-dimensional discrete signals in the complex domain, which are widely used in communication, radar, sonar, and information security to complete the requirements for synchronization, multiple random access, channel estimation, ranging, anti-interference, and digital watermarking due to their anti-interference, stability, and easy implementation. There are close relations between sequences and mathematical objects such as cyclic Hadamard matrices, difference sets (families), tight frames, unbiased bases, and cyclic codes. Constructing sequences reaching or approximating the theoretical bounds has always been a core topic in sequence design and coding theory. In this paper, based on the Semi-Bent function and difference set, we propose a class of optimal ternary sequence sets (the elements of sequences belong to $\{0,\pm~1\}$), which is the first class of optimal sequence set strictly achieving the Welch bound since this bound was established in 1974. Compared with the binary sequence sets (the elements of sequences take values $\pm~1$), the new sequence set is more suitable for ultra-wideband communication, digital watermarking, and spectrum constrained scenarios. While compared with known ternary sequence sets asymptotically approaching two times the Welch bound, the proposed ternary sequence sets have better correlation properties.

Design and implementation of sequential excitation module for high fidelity piezoresponse force microscopy

The acquisition of accurate information through a contact resonance mode is critical for mapping weak electromechanical effect reliably by using piezoresponse force microscopy (PFM). However, it is very challenging to track resonance frequency shifting when the contact stiffness from the sample varies significantly. In this work, we have developed a sequential excitation (SE) module to enable high fidelity PFM. A customized discrete frequency sweep signal from an arbitrary waveform generator is used for drive excitation so that resonance frequency tracking is no longer necessary. Furthermore, the AC component of the piezoresponse is sampled by using an oscilloscope instead of using lock-in amplifiers. To accommodate high volume of data acquisition, a fast analysis method is also developed to fit the transfer function of the cantilever efficiently on the fly during scanning. Hardware implementation and data processing are described in detail. The capability of our SE module has been demonstrated on an ordinary PMN-PT film via first and second harmonic PFM, as well as a suspended freestanding MoS2 membrane that is very challenging to probe due to its substantial variation in contact stiffness.

Systems of Discrete Walsh-Like Sequential Functions

In this paper the algorithm for constructing the discrete (0,1)-sequent functions constituting the whole symmetric systems of orthogonal equidistant functions on the example of the eighth-order systems developed. Discrete sequential functions form by replacing their piecewise constant values +1 or -1 in the time domain (from the original space) with numerical values 0 and 1 in the image space. We refer to Walsh-like functions as (0,1)-sequent functions in which the number of zeros and ones in each half of the definition interval is not necessarily the same as in classical Walsh functions. By the directed search method, each of the 30 formed whole groups of equidistant sequent functions unfolds, like the group of classical Walsh functions of the eighth order, into 28 symmetric systems of sequent functions. The main result achieved in this work should consider an expansion of the set of Walsh-like systems of the eighth order by more than an order of magnitude. The algorithm's simplicity for synthesizing such systems of sequential functions and the high speed of spectral processing of discrete signals provided by the proposed bases open the Walsh-like systems for broad prospects of application in various fields of science and technology.

Real-Time Optimization of Social Distancing to Mitigate COVID-19 Pandemic Using Quantized Extremum Seeking

The application of extremum seeking control is investigated to mitigate the spread of the COVID-19 pandemic, maximizing social distancing while limiting the number of infections. The procedure does not rely on the accurate knowledge of an epidemiological model and takes realistic constraints into account, such as hospital capacities, the observation horizon of the pandemic evolution and the quantized government sanitary policy decisions. Based on the bifurcation analysis of a SEIARD compartmental model providing two possible types of equilibria, numerical simulation reveals the transient behaviour of the extremum of the constrained cost function, which, if rapidly caught by the algorithm, slowly drifts to the steady-state optimum. Specific features are easily incorporated in the real-time optimization procedure, such as quantized sanitary condition levels and long actuation (decision) periods (usually several weeks), requiring processing of the discrete control signal saturation and quantization. The performance of the proposed method is numerically assessed, considering the convergence rate and accuracy (quantization bias).

Enhancing Prony’s method for fault location

The paper presents a phasor estimator combining Prony’s method and discrete analytic signal generation for use in impedance-based fault location. The precision of impedance-based fault location hinges on accurately extracting the fundamental component in the presence of transient components, including inter-harmonics, which compromises the accuracy of the industry-adopted full-cycle Discrete Fourier Transform (DFT) method. The analytic signal gives rise to half the model order, excluding the purely damped exponential, thus producing more accurate results from Prony’s process while also contributing to its speedup. The discrete analytic signal is generated so that its length is half of the original signal, meaning its sampling frequency is effectively halved, yielding better numerical conditioning and faster processing in Prony’s method. The proposal does not trade accuracy for speed, yet the speed up makes fault location closer to the vision of installing its software module on protection devices. The proposed Prony’s method with discrete-time analytic signals is compared with the classical Prony’s method applied to discrete-time real-valued signals, the full-cycle DFT with special provisions for eliminating the decaying DC component, and Kung’s method. The results obtained by the different approaches show the superiority of Prony’s method when combined with analytic signal generation.

Soliton-mediated ionic pulses and coupled ionic excitations in a dissipative electrical network model of microtubules

Many cellular activities are mediated by microtubules (MTs), with most electrophysiological processes depending on ionic flow through MT cylinders. This paper addresses such conductive features by representing the MT as a nonlinear electrical transmission line composed of capacitive and dissipative properties. Thanks to the semi-discrete approximation near the continuum limit, coupled ionic pulses flowing along cellular microtubules are described by a set of coupled cubic complex Ginzburg-Landau (CGL) equations whose one of the solutions is a plane wave. The stability of the latter is checked, under weak modulation, using an explicit analytical expression for the modulational instability (MI) growth rate. The parametric analysis of the instability growth rate allows detecting parameter regions where ionic conductivity, through modulated waves, in the MT network is likely to occur. Dissipative bright-bright pulse soliton solutions for the nonlinearly coupled cubic CGL equations are constructed using a modified Hirota's bilinear method. A generalized coupled mode for the discrete ionic signal is proposed and used as the initial condition to be propagated in the nonlinear electrical transmission lattice of MT under direct numerical simulations. The ionic pulse transfer, mediated by the nonlinear interaction between oscillatory modes, is manifested by the formation of trains of modulated waves whose behaviors depend on the right choice of system parameters. Those results theoretically suggest that coupled ionic signals may facilitate information processing involving MTs.

Stability of switched stochastic reaction–diffusion systems

As one of important hybrid dynamical systems, switched system has practical applications in some practical systems. Generally, switched system is made up of a family of continuous-time subsystems and discrete switching signals. Affected by environmental disturbance, stochastic switched system should be considered. This paper deals with a class of switched stochastic reaction-diffusion systems (SSRDSs, in short), where the discrete switching signal is a right continuous and piecewise function. The switching instants are stopping times or deterministic times. Criterions on stability in probability and exponential stability in mean square of the trivial solution for SSRDSs are derived by means of Lyapunov functional methods. We propose two examples to verify the obtained theoretical results.

Planar Rainbow Refractometry For Size, Refractive Index And Position Measurement Of Droplets In A Plane

Rainbow refractometry can simultaneously measure the temperature and geometric parameters of droplets by analyzing the recorded primary rainbow scattering signal of the droplet. The technique therefore has high potential in measurement applications involving reacting/non-reacting sprays. This study develops the planar rainbow refractometer technique, expanding the measurement dimension from a single "line" measurement to a "planar" measurement. The position of the droplet in the plane is determined by the contour of the rainbow signal, whereas the size and refractive index of the droplet are derived from the extracted rainbow image using the calibrated scattering angle. A simple and compact rainbow optical measurement system is constructed based on horizontal slit modulation, enabling the recording of spatially discrete rainbow signals of droplets in a plane. A novel scattering angle calibration method using a precisely traversed monodisperse droplet stream with a priori parameters is proposed and the algorithm for obtaining the calibration coefficients is evaluated by simulation. Spray verification experiments were carried out. The signal processing consists of image recognition, particle localization, and the rejection of non-spherical droplets. The possibility of estimating droplet number density is also discussed.

Finite-time stability analysis of switched stochastic reaction-diffusion systems

In this work, we consider a class of switched stochastic reaction-diffusion systems (SSRDSs, in short), where the discrete switching signal is a right continuous, piecewise function and the switching instants are stopping times or deterministic times. Criteria on finite-time stability in the probability of the trivial solution for SSRDSs are derived by means of Lyapunov functional methods. We propose an example to verify the obtained theoretical results.

A minimum SNR criterion for computed tomography object detection in the projection domain.

A common rule of thumb for object detection is the Rose criterion, which states that a signal must be five standard deviations above background to be detectable to a human observer. The validity of the Rose criterion in CT imaging is limited due to the presence of correlated noise. Recent reconstruction and denoising methodologies are also able to restore apparent image quality in very noisy conditions, and the ultimate limits of these methodologies are not yet known. To establish a lower bound on the minimum achievable signal-to-noise ratio (SNR) for object detection, below which detection performance is poor regardless of reconstruction or denoising methodology. We consider a numerical observer that operates on projection data and has perfect knowledge of the background and the objects to be detected, and determine the minimum projection SNR that is necessary to achieve predetermined lesion-level sensitivity and case-level specificity targets. We define a set of discrete signal objects that encompasses any lesion of interest and could include lesions of different sizes, shapes, and locations. The task is to determine which object of is present, or to state the null hypothesis that no object is present. We constrain each object in to have equivalent projection SNR and use Monte Carlo methods to calculate the required projection SNR necessary. Because our calculations are performed in projection space, they impose an upper limit on the performance possible from reconstructed images. We chose to be a collection of elliptical or circular low contrast metastases and simulated detection of these objects in a parallel beam system with Gaussian statistics. Unless otherwise stated, we assume a target of 80% lesion-level sensitivity and 80% case-level specificity and a search field of view that is 6 cm by 6 cm by 10 slices. When contains only a single object, our problem is equivalent to two-alternative forced choice (2AFC) and the required projection SNR is 1.7. When consists of circular 6-mm lesions at different locations in space, the required projection SNR is 5.1. When is extended to include ellipses and circles of different sizes, the required projection SNR increases to 5.3. The required SNR increases if the sensitivity target, specificity target, or search field of view increases. Even with perfect knowledge of the background and target objects, the ideal observer still requires an SNR of approximately 5. This is a lower bound on the SNR that would be required in real conditions, where the background and target objects are not known perfectly. Algorithms that denoise lesions with less than 5 projection SNR, regardless of the denoising methodology, are expected to show vanishing effects or false positive lesions.

Graph-Embedded Convolutional Neural Network for Image-Based EEG Emotion Recognition

Emotion recognition from electroencephalograph (EEG) signals has long been essential for affective computing. In this article, we evaluate EEG emotion recognition by converting EEG signals from multiple channels into images such that richer spatial information can be considered and the question of EEG-based emotion recognition can be converted into image recognition. To this end, we propose a novel method to generate continuous images from discrete EEG signals by introducing offset variables following a Gaussian distribution for each EEG channel to alleviate the biased electrode coordinates during image generation. In addition, a novel graph-embedded convolutional neural network (GECNN) method is proposed to combine the local convolutional neural network (CNN) features with global functional features to provide complementary emotion information. In GECNN, the attention mechanism is applied to extract more discriminative local features. Simultaneously, dynamical graph filtering explores the intrinsic relationships between different EEG regions. The local and global functional features are finally fused for emotion recognition. Extensive experiments in subject-dependent and subject-independent protocols are conducted to evaluate the performance of the proposed GECNN model on four datasets, i.e., SEED, SDEA, DREAMER, and MPED.

Требования к кодирующей матрице фазокодоманипулированного зондирующего сигнала с нулевой зоной автокорреляции.

Optimal discrete signals does not allow solving the problem of radar range resolution for echo signals overlapping in time with significantly different amplitudes. Also, these signals limit the possibility of improving the quality of the radar image in radar of different applications due correlation noise. Therefore, to solve the above problem, it is of interest to use a probing signal with a zero autocorrelation zone. To form an autocorrelation function with a zero sidelobes region, the probing signal must be a pulse train of two or more phase-code-manipulated pulses. It is analytically substantiated in the paper that in order to form a zero autocorrelation zone, a pulse train of pulses must be coded by an ensemble of complementary or orthogonal sequences. In this case, the probing signal will have a large number of pulses in a pulse train, which makes it difficult to use it in a radar with a common transmitting and receiving antenna. It is shown that when coding by an ensemble of complementary sequences, the complex envelopes of all discrete pulses in a pulse train must be equal. In this case, the compressed signal will have a sufficiently high sidelobe ratios in a zero autocorrelation zone with Doppler mismatch. It has also been analytically proved that in order to form a zero autocorrelation zone, a pulse train of pulses can be coded by rows of a block matrix, consisting of a set of mutually orthogonal matrices. Then the complex envelopes of discrete pulses in a pulse train can be different, which makes it possible to suppress the level of sidelobes in a zero autocorrelation zone with Doppler mismatch. The paper also contains the requirements for the coding matrix of a polyphase (p-phase, where р ≥ 2 – prime number) probing signal with a zero autocorrelation zone, consisting of a minimum number of pulses in a pulse train equal to p, called a coherent complemented signal.

Информационные технологии на основе шумоподобных сигналов: II. Cтатистические и фрактальные свойства хаотических алгоритмов

On the basis of nonlinear systems with dynamic chaos, discrete chaotic signals with high information capacity have been developed and studied. The influence of the main parameters of a generating chaotic algorithm with delay on the statistical, correlation, structural and fractal characteristics of non-periodic pseudo-random integer and binary sequences generated by the algorithm is analyzed by numerical methods. It is shown that non-periodic pseudo-random sequences (PRS) generated by a chaotic algorithm with delay, for all values of the main parameters, have good statistical, correlation, structural and fractal characteristics, close to random sequences of independent trials. It is shown that these characteristics are provided on a long PRS cycle in a multidimensional phase space for all the main parameters of the chaotic algorithm and an arbitrary choice of initial conditions. Such binary PRSs can be quite effectively used in telecommunication systems using streaming coding of large blocks of information messages from the point of view of secrecy, noise immunity and cryptographic stability of the communication channel.

A Two-Stage DNN Model With Mask-Gated Convolution for Automotive Radar Interference Detection and Mitigation

As the number of radar sensors on the road increases rapidly and many of these sensors share the same frequency spectrum, mutual interference cannot be avoided. This paper introduces a novel automotive radar interference mitigation approach using an autoencoder model which consists of separate neural networks for the detection and reconstruction steps. A mask-gated convolution is proposed to help the reconstruction neural network to learn the signal pattern from interference-free samples and to interpolate accordingly the signal segments at the disturbed positions. Through perturbation analysis it is shown that the reconstruction neural network can recover the distorted samples by utilizing their surrounding relevant samples. By exploiting the nature of interference in real-world scenarios, the proposed training approach does not need hand-labeled training data. Together with the proposed composite training loss, the neural network can recover the disturbed discrete beat signal with remarkable improvements in the signal-to-interference-plus-noise ratio (SINR) and the mean absolute percentage error (MAPE). Moreover, despite the use of a purely simulated training data set, the autoencoder can deal with real-world radar measurements which are more complex than the training data set.

Dynamic diagnosis method and quantitative characterization of rail corrugation

This paper describes a dynamic and quantitative method of diagnosing and estimating rail corrugation in railway tracks using acceleration data obtained from high-speed comprehensive inspection train. Although the amplitude of rail corrugation is small, it will arouse violent vibration between the wheel and rail under high-speed conditions, and accelerate the structural damage of track-vehicle system components. Combined with high-frequency Axle Box Acceleration (ABA), a time-frequency analysis-based Rail Corrugation Index and Energy Factor method are proposed to diagnose the rail corrugation of high-speed railway. The corrugation amplitude is estimated by the quadratic integral of filtered ABA. The new evaluation method uses the windowed energy index signal of the ABA to replace the original signal, and demodulates the high-frequency discrete response signal into a stable low-frequency energy signal without losing the vibration characteristics. Inverse SSTFT is applied to estimate the amplitude of rail corrugation. High-speed railway application results show that the proposed index can effectively diagnose the rail corrugation dynamically and quantitatively and estimate the degree of it.

Psychological Mobilization of Innovative Teaching Methods for Students' Basic Educational Curriculum Reform Under Deep Learning.

Educational innovation reform is used as the background. In response to the need to propose innovative educational programs, the concepts of Distributed Deep Neural Network (DDNN) and deep learning under edge computing are used as the basis. A teaching program for Science Technology Engineering Mathematics (STEM) is proposed. The average training method is used to verify the performance of the model. Sampling rate means the number of samples per second taken from a continuous signal to form a discrete signal. The accuracy and sample ratio obtained are higher than 95%. The communication volume is 309 bytes, which is in a good range. On this basis, a university uses STEM teaching plans and questionnaires to influence the psychological mobilization factors of students' deep learning effects. Challenging learning tasks and learning motivation have the greatest impact on deep learning, and conclusions that both are positive effects are obtained. Therefore, STEM innovative teaching programs can be widely used. The plan provides a reference theory for improving teaching innovation in the context of the basic educational curriculum reform in China. STEM curriculum is the dual subject of teachers and students, and the learning community includes multi-stakeholders. There are hierarchical relationships among the subjects. In terms of financial support, the first two funds come from the school. Learning communities have dedicated sponsorship partners complemented by clear financial planning. There is not much difference in course resources. Still, the learning community will provide more diversified media forms and special websites, and other auxiliary resources are open to all users. They can obtain first-hand resources without applying. In terms of project form, in addition to the core classroom teaching, the latter two can provide richer activities and realize the diversity of time, space, and information exchange.

SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES.

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples the roles of scale and frequency, replacing wavelets with Gabor-type measurements. We show that, with suitable nonlinearities, our measurements distinguish Poisson point processes from common self-similar processes, and separate different types of Poisson point processes.

ARC High Order Filters Suitable for Antialiasing and/or Reconstruction Filters

The discrete time signal processing circuit requires an anti-aliasing filter at the input and a reconstruction filter at the output, generally. In this paper, selected basic structures of some active filters are described and compared with a view to the degradation of the attenuation over the transient frequency of the operational amplifier. Firstly, the reasons for the degradation of the attenuation are explained theoretically. Secondly, these conclusions are verified by simulations. These simulations were performed by spice-like circuit simulator MicroCap version 11.