Analytically estimated topological characteristics of the region of complex irregular oscillations in the parameter space of a double-circuit self-oscillator

An analytic basis (system of equations and limiting conditions) is developed to determine the configuration, location, and dimension of the region of intense irregular (on limited time intervals) oscillations in the 3D space of the generalized parameters of a double-circuit transistor self-oscillator. It is demonstrated that self-contained double-circuit systems can exhibit the oscillation-modulation instability of regular oscillations. In the presence of strong (trigonometric) nonlinearities that contain a phase as the argument of nonlinear functions, the instability gives rise to intense irregular oscillations. The boundaries of the region of the oscillation-modulation instability are analytically determined in the parameter space of the given system under the condition for the overlapping of partial spectra. The analytically calculated instability region is compared with the computer-calculated specific regions of various complex oscillations. It is demonstrated that, at certain practically acceptable limitations, the boundaries of the analytic region can be used for the estimation of the domain of existence of complex intense irregular oscillations in self-oscillators.     

Characterization and parameterization of dynamic wireless channels over long duration using evolutionary channel parameters

The characterization and parameterization of processes that arise in many fields of science and technology are very crucial. Of particular importance are dynamic processes whose statistics are time‐varying and are often modeled as stochastic processes. A typical example of such process is the wireless communication channel. Existing methods that are used to characterize and parameterize the dynamic stochastic wireless channel often consider short‐term duration over which the channel statistics are invariant. Conversely, this paper presents the characterization of the dynamic wireless communication channel over a long‐term duration where time/frequency channel realizations are obtained at sample intervals. To structure such channel realizations over a long duration, the idea of concatenating the ‘instantaneous’ channel realizations is presented. The resultant concatenated multivariable process is characterized using the concepts of process non‐summability and piecewise separability. Based on these concepts, the second‐order statistical parameterization of the concatenated stochastic process in both time and frequency domain is presented. The parameterization approach is based on fitting appropriate set of unit step functions that approximate the raw concatenated data using sets of evolutionary stationarity parameters. To illustrate the concepts developed in this paper, measurement‐based experiments and analysis are presented and adaptively applied to improve wideband multicarrier system performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Function minimization using Boolean matrices

A simple and computationally effective method is suggested for the minimization of the switching functions that also include “don't care” terms. The method is based upon the use of Boolean matrix representation of the function. The procedure is suitable for large variable functions, for computer and hand simulation. This paper also describes a computer simulation which helps in the detection of the final decomposition for a given switching function; three such realizations are described using hand simulation and another three realizations using computer simulation.     

探测人体呼吸的多普勒搜救雷达数字信号处理

描述了相干多普勒雷达人体呼吸回波信号的试验研究结果,给出了信息处理的频谱与时域实现及其统计特性。试验表明,在微波频段的声音信号中,人体呼吸引起的回波信号相位调制产生的过程具有周期性关联随机过程的特性。基于等距栅格对该过程的统计特性进行计算,其周期与过程关联周期相等。文中提出了一种随机准则来估算关联周期。对基于等距栅格的过程的遍历性作了理论验证和试验证实。     

Adaptive parallel-cascade truncated Volterra filters

This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realizations implement higher order Volterra systems as a parallel connection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experiments. The experimental results indicate that the normalized LMS adaptive parallel-cascade Volterra filter has superior convergence properties over several competing structures. This paper also includes an experiment that demonstrates the capability of the parallel-cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system     

Identification of time-varying biological systems from ensembledata [joint dynamics application]

The theory underlying a new method for the identification of time-varying systems is described. The method uses singular value decomposition to obtain least-squares estimates of time-varying impulse response functions from an ensemble of input-output realizations. No a priori assumptions regarding the system structure or form of the time-variation are required and there are few restrictions on the input signal. Simulation studies, using a model of time-varying joint dynamics, show that the method can track rapid changes in system dynamics accurately and is robust in the presence of output noise. An application of the method is demonstrated by using it to track dynamic ankle stiffness during a rapid, voluntary, isometric contraction. During the transient phase of the contraction, low-frequency ankle stiffness gain decreased in a manner which could not be described with the second-order model of joint dynamics often used under stationary conditions.     

Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics

A novel class of special functions for electromagnetics is presented. Formed by the incomplete Hankel and modified Bessel functions, this class allows solving electromagnetics problems concerning truncated cylindrical structures. The differential and recurrence equations of these functions feature additional terms with respect to the classical theory of the Hankel and Bessel functions. The general properties, the most important analytical characteristics, and the large argument asymptotic approximations of the incomplete functions are derived using the steepest descent path (SDP) technique, showing that each special function splits into two terms. The first one has a discontinuous character and is linked to the saddle-point(s) contribution(s), while the second one, arising from the integral end-point contribution(s), compensates exactly the said discontinuity. In the solution of electromagnetic problems, the first term describes the geometrical optics (GO) field, the diffracted field being described by the second one. The general theory is employed to find the closed form analytical solution of the field radiated from a uniform line current source. Using the properties of the incomplete Hankel functions, it is demonstrated that this source excites cylindrical fields having optical character. Finally, the shape of the spatial regions where the GO solution cannot be applied is determined and discussed in details.     

Fisher information with respect to cumulants

Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a physically compelling interpretation of representing the highest precision with which the first cumulant of the random variable, i.e., its mean, can be estimated from its statistical realizations. We construct a complete hierarchy of information measures that determine the best precision with which all of the cumulants of a random variable-and thus its complete probability distribution-can be estimated from its statistical realizations. Several properties of these information measures and their generating functions are discussed.     

Tomographic reconstruction and estimation based on multiscalenatural-pixel bases

We use a natural pixel-type representation of an object, originally developed for incomplete data tomography problems, to construct nearly orthonormal multiscale basis functions. The nearly orthonormal behavior of the multiscale basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. In addition, the coarsest scale elements of this matrix capture any ill conditioning in the system matrix arising from the geometry of the imaging system. We exploit this feature to partition the system matrix by scales and obtain a reconstruction procedure that requires inversion of only a well-conditioned and sparse matrix. This enables us to formulate a tomographic reconstruction technique from incomplete data wherein the object is reconstructed at multiple scales or resolutions. In case of noisy projection data we extend our multiscale reconstruction technique to explicitly account for noise by calculating maximum a posteriori probability (MAP) multiscale reconstruction estimates based on a certain self-similar prior on the multiscale object coefficients. The framework for multiscale reconstruction presented can find application in regularization of imaging problems where the projection data are incomplete, irregular, and noisy, and in object feature recognition directly from projection data.     

Nonlinear excitation of ultrasound in a two-layer ferrite structure under ferromagnetic resonance conditions

The nonlinear problem of excitation of hypersound in a normally magnetized structure is considered. The structure consists of two ferrite layers, its elastic properties are constant across the entire structure thickness, and the magnetic properties of the layers can be different. The equations of motion and boundary conditions for the magnetization components and elastic displacement are obtained for the case of an arbitrary angle of the magnetization vector precession. Using the decomposition in eigenmodes, the problem is reduced to a system of an infinite number of second-order differential equations. In the case when the first elastic mode is excited, the complete problem is reduced to a system of thirty nonlinear first-order differential equations solved numerically by means of the Runge-Kutta method. The time evolution and amplitude-frequency characteristics of excited oscillations are considered. Conditions under which the amplitude of nonlinear-mode elastic vibrations exceeds the amplitude of linear-mode elastic vibrations by a factor as large as 70 and the bandwidth increases by a factor as large as five are revealed.     

On the Regular and Irregular Spiking Behaviour of Solid-state Lasers†

A solid-state laser with plane parallel end faces usually produces an output which exhibits spikes in a random manner, whereas the prevalent quantum relaxation theory predicts regular relaxation oscillations. Recently in a new theoretical approach, the author has shown that in an imperfect crystal the filamentary nature of the laser action is postulated by the classical physics. A single filament generates relaxation oscillations as predicted by the familiar theory, and the irregular spiking may then be considered a superposition of outputs from several filaments. This model is supported by many experimental observations and it suggests o re-enterpretation of certain experimental data published.

The field distributions in a Fabry-Perot resonator with a sufficiently large Fresnel number can be expressed in terms of parabolic cylinder functions. The mode volume of a low-order eigenmode is considerably smaller than the crystal volume. Accounting for this fact in the quantum relaxation theory yields that the decay time constant of the relaxation oscillations is actually smaller than predicted by the linearized Statz and deMars rate equations. This is in favourable agreement with the experiment.     

Transmission of information masked with an irregular signal via a radio channel

A scheme for transmission of information masked with an irregular signal (chaotic oscillations) is considered. Mathematical models are developed for communications systems in which chaotic oscillations are radiated in two frequency bands separated owing to mixing of regular and chaotic oscillations. Results of numerical analysis and physical experiments are presented. The possibility of confidential transmission of an information signal is demonstrated.     

Multiple frequency transformation in the magnetostriction transducer: Frequency division in the relaxation mode

The forced oscillations of the magnetization and elastic displacement in the normally magnetized ferrite plate with magnetoelastic properties are discussed. The process whereby the initial frequency is divided in the ratio defined by the multiplicity of the resonance frequencies of magnetic and elastic subsystems is investigated. The time and amplitude characteristics of the phenomenon are revealed on the basis of the impact excitation model of an elastic system under short-term magnetic actions. Recommendations are given for the practical implementation of excitation-frequency division in the scheme of a magnetostriction transducer.     

Interconversion between truncated Cartesian and polar expansions of images.

In this paper, we propose an algorithm for lossless conversion of data between Cartesian and polar coordinates, when the data is sampled from a 2-D real-valued function (a mapping: R2 --> R) expressed as a particular kind of truncated expansion. We use Laguerre functions and the Fourier basis for the polar coordinate expression. Hermite functions are used for the Cartesian coordinate expression. A finite number of coefficients for the truncated expansion specifies the function in each coordinate system. We derive the relationship between the coefficients for the two coordinate systems. Based on this relationship, we propose an algorithm for lossless conversion between the two coordinate systems. Resampling can be used to evaluate a truncated expansion on the complementary coordinate system without computing a new set of coefficients. The resampled data is used to compute the new set of coefficients to avoid the numerical instability associated with direct conversion of the coefficients. In order to apply our algorithm to discrete image data, we propose a method to optimally fit a truncated expression to a given image. We also quantify the error that this filtering process can produce. Finally the algorithm is applied to solve the polar-Cartesian interpolation problem.     

MAP estimation of finite gray-scale digital images corrupted bysupremum/infimum noise

Finite gray-scale digital images are modeled as realizations of discrete random functions (DRF), and then the estimation of realizations of DRF corrupted by a supremum/infimum noise model is considered. It is proved that morphological operators such as openings, closings, supremum of openings and infimum of closings are optimal maximum a posteriori (MAP) estimators under an appropriate and minimal set of assumptions relating to the structural and statistical constraints on image DRF and noise DRF. These results are obtained for independent, identically distributed (i.i.d.) noise for single and multiframe observation scenarios. Next, the assumption of i.i.d. noise is relaxed and the MAP optimality and strong consistency of morphological filters for filtering image DRF degraded by morphologically smooth noise (i.e., colored noise) is proved. Simulations on actual image data are carried out in support of the validity of theoretical results presented.     

Minimal positive realizations for a class of transfer functions

It is a standard result in linear-system theory that an nth-order rational transfer function of a single-input single-output system always admits a realization of order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e. a positive system), and it is known that this restriction may force the order N of realizations to be strictly larger than n. In this brief we present a class of transfer functions where positive realizations of order n do exist. With the help of our result we give improvements on some earlier results in positive-system theory.     

Quasi-periodic Faraday-rotation fluctuations of the polarization plane during radio sounding of the circumsolar plasma

The statistical characteristics of Faraday-rotation fluctuations (FRFs) of a radio-wave polarization plane are analyzed when the circumsolar plasma is sounded by the signals of a Helios 1 space probe. The time spectra and auto- and crosscorrelation functions of FRFs, which are measured simultaneously at two ground stations separated by large distances, have been determined. The wavelet spectra of FRFs are presented, and the opportunities of the wavelet transform and other techniques used to reveal quasi-periodic FRFs with different periods are investigated. It is demonstrated that the quasi-periodic magnetic field oscillations, which are excited by the trains of Alfvén waves propagating through the solar supercorona (their period varies between 2 and 160 min), are observed at the heliocentric distances of 3–12 solar radii.     

Complex oscillations in a double-circuit self-oscillator built on a field-effect transistor on the basis of the inductive three-point circuit

The existence of irregular complex oscillations in a double-circuit self-oscillator built on a field-effect transistor on the basis of the inductive three-point circuit is revealed. The dynamics of the circuit model is analyzed by means of a computer simulation program for construction of the boundaries of the regions of complex oscillations existing in several parameter planes of the system and for determination of the parameters corresponding to the highest intensity of complex oscillations. The necessary conditions for excitation of complex oscillations are obtained in the form of restrictions imposed on the values of the so-called active and passive Q factors of the transistor drain circuit. The value of the allowable external load in the oscillating loop of the drain circuit is estimated from the viewpoint of excitation of complex oscillations.     

门控递归神经网络处理不规则时间序列数据综述

随着多传感器系统的发展以及非结构化手工数据记录机制的持续使用,不规则时间序列数据越来越普遍。不规则数据和由此产生的缺失值严重限制了对数据进行分析和建模以完成分类和预测任务的能力。通常情况下,用于处理时间序列数据的传统方法会引起偏差,并对底层数据的生成过程进行强假设,这可能会导致较差的模型预测结果。传统的机器学习和深度学习方法虽仍处于数据建模的前沿,但最多只能受到不规则时间序列数据集的影响,无法对不完整时间序列的时间不规则性进行建模。门控递归神经网络(RNN),如LSTM 和GRU,在序列建模方面取得了突出的成绩,并在许多应用领域得到了应用,如自然语言处理。这些模型已成为时间序列建模的良好选择,也是处理不规则时间序列数据的重要工具。文中重点介绍了处理不规则时间序列数据的两种常用方法,即在数据预处理阶段输入缺失值以及在学习过程中修改算法从而直接处理缺失值,旨在介绍这一研究分支中出现的有效的技术,以便研究人员创造出进一步处理不规则时间序列数据的新技术。     

Multiwave interaction of an ensemble of self-oscillators in a two-dimensional wave field with inhomogeneous boundary

A numerical experiment is used to analyze specific features of oscillations of the field excited by an ensemble of self-oscillators in 2D circular and segment-shaped regions. Parameter domains are found in which coherent oscillations are formed in the considered system in the self-consistent operation mode. It is shown that, if oscillations with large azimuthal number are excited, the space-time structure of the wave process can have a high degree of time coherence and a fractal-shaped spatial distribution.