用于计算离散分数阶傅立叶变换的MA-CDFRFT算法改进

基于中心类型DFT矩阵特征分解的MA-CDFRFT(Multiangle Centered Discrete Fractional Fourier Transform)算法在计算一组离散分数阶傅立叶变换DFRFT(Discrete Fractional Fourier Transform)时充分利用FFT运算来减小运算量。结合偶数点离散傅立叶变换DFT(Discrete Fourier Transform)运算的对称性原理，通过数学推导将MA-CDFRFT算法中的一维对称性扩展到频率和变换阶数的二维平面上。利用这个二维对称性原理，改进算法将原算法的主要计算量减小了一半左右。仿真测试结果证明了改进算法的正确性。     

Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. Many theories for this transform are already known, but the uniform sampling theorem, as well as the sampling rate conversion theory about arbitrary lattices sampling in the LCT domain are still to be determined. Focusing on these issues, this paper carefully investigates arbitrary lattices sampling, the sampling with separable matrices and nonseparable matrices, to obtain uniform sampling theorem and the sampling rate conversion theory in the LCT domain. Firstly, the spectral expression of the discrete-time signal sampled via arbitrary lattice is deduced in the LCT domain. Based on it we propose the alias-free sampling relationship between two matrices and present the perfect reconstruction expressions for bandlimited signals in the LCT domain. Secondly, for further research on discrete signals to obtain sampling rate conversion theory, we define the multidimensional discrete time linear canonical transform (MDTLCT), as well as the convolution for the MDTLCT. Thirdly, the formulas of multidimensional interpolation and decimation via integer matrices in the LCT domain are derived. Then, based on the results of interpolation and decimation, we make analyses of the sampling rate conversion via rational matrices in the LCT domain, including spectral analyses and the formulas in time domain. Finally, simulation results and the potential applications of the theories are also presented.     

Recursive reconstruction of sequences from group-delay

A recursive procedure to reconstruct a given sequence from its group delay or phase derivative is given. The procedure is based on the relationships between minimum, maximum phase sequences and their cepstra, and on the modified least squares (MLS) rational approximation. To avoid unwrapping of the phase, the cepstrum of the sequence is calculated from the group delay function. Using a recursive procedure, we find from the cepstrum values a minimum phase sequence with a phase equal to that of the original sequence. The reconstructed sequence is obtained using the MLS procedure to find recursively a rational approximation of the minimum phase sequence. The constraints under which the phase reconstruction is possible are checked with a root distribution algorithm, and we indicate how to modify the sequence when the constraints are not satisfied. Examples illustrate the efficiency of the proposed procedure.     

Event-based bipartite consensus of second-order discrete-time multi-agent systems with matrix-weighted signed networks

This article researches the bipartite consensus for discrete-time second-order multi-agent systems on matrix-weighted signed networks, which can describe the inter-dependencies of multidimensional states among states. So as to save limited communication resources, based on the matrix-weighted combined measurements of the position and velocity states, a matrix-weighted event-triggered control algorithm is designed. With the help of the stability theory, variable transformation and the inequality technique, the bipartite consensus conditions which are based on coupling gains, discrete interval, the parameters in the event-triggered rule and communication topology are obtained. Furthermore, the conditions to avoid the controller updating in each discrete-time are supplied. At last, a simulation example is offered to demonstrate the theoretical results.     

基于特征矢量稀疏分解的非圆信号DOA估计

文中提出当信源为非圆信号时,基于特征矢量稀疏分解进行DOA估计;并在稀疏恢复过程中,比较空间范数变化对误差的影响.该方法对协方差矩阵进行了扩展,在利用L曲线方法自适应得到正则化参数的同时,对空间范数应用进行了推广.不仅提高信息利用率,能够处理相干信号源,而且不需要已知信号源数目,性能优于平滑处理过后的NC-MUSIC算法.     

Event-triggered bipartite leader-following consensus of second-order nonlinear multi-agent systems under signed digraph

This paper investigates the bipartite leader-following consensus of second-order multi-agent systems with signed digraph topology. To significantly reduce the communication burden, an event-triggered control algorithm is proposed to solve the bipartite leader-following consensus problem, where a novel event-triggered function is designed. Under some mild assumptions on the network topology and node dynamics, a sufficient condition is derived using Lyapunov stability method and matrix theory to guarantee the bipartite consensus. In particular, it is shown that the continuous communication can be avoided and the Zeno-behavior can be excluded for the designed event-triggered algorithm. Numerical simulations are presented to illustrate the correctness of the theoretical analysis.     

Fixed-time bipartite consensus of nonlinear multi-agent systems under directed signed graphs with disturbances

This paper considers the fixed-time bipartite consensus of nonlinear multi-agent systems (MASs) subjected to external disturbances. Under the directed signed networks, several sufficient conditions are proposed to guarantee the fixed-time bipartite consensus of MASs with or without leaders, respectively. Some discontinuous control protocols are developed to realize fixed-time tracking bipartite consensus of MASs with a leader. Moreover, the fixed-time leaderless bipartite consensus under directed signed graph are discussed as well. Two numerical examples are given to verify the effectiveness of the theoretical results.     

Quantifying the structural and temporal characteristics of negative links in signed citation networks

Although the citation relationships among papers can help in tracking and understanding the development of knowledge, few studies have noted that the content and sentiments of citations of a paper differ. Here, we use sentiment-labeled citation data to construct a directed signed citation network, in which an author may agree with or criticize the cited paper and these represent different ways of inheriting knowledge. The dataset we use consists of 9,038 papers in the field of Computational Linguistics, including 25,275 citations, with 20.8% positive citations, 8.6% negative citations and 70.6% neutral citations. We systematically quantify the structural patterns of negative citations, impact assortativity of involved papers, occurrence time distribution and consequences of receiving negative attention. Remarkably, we find that papers with different impacts have a similar probability of receiving negative citations, and highly cited papers tend to give negative citations to low-impact papers around but avoid giving negative citations to high-impact papers. Our research also reveals the random occurrence rules and colocation patterns of negative citation distribution. In addition, we show that, in the short term, around 60% of multiple negative citations is positively related to the impact of the cited paper while more than 80% are negatively related to the impact in the long run. Our findings explain the pattern by which negative citations occur and deepen the understanding of negative citations.     

Simulation of modulated signals

A new formulation for the simulation of modulated signals based on a generalized structure is presented. In this approach a modulated signal is characterized in terms of a time-varying system whose differential equation is simulated. Algorithms presented in the paper may also be used to track signal parameters such as the envelope and the carrier. This concept is illustrated by several algorithms of AM and FM simulators.     

Control of clock signals

Precision and reliability of timescales are of importance in many situations, in particular in satellite navigation systems (i.e., Galileo system). Motivated by the necessity to improve the precision and the reliability of such clock signals, we have explored the possibility to exploit control theory in clock steering methods. First of all we provide a more robust theoretical framework for the analysis of the process. Two novel control algorithms are here proposed aiming to meet metrological specifications. Numerical simulations have been performed in order to evaluate the performances of the new control systems.     

Extraction of motor unit action potentials from electromyographic signals through generative topographic mapping

The extraction of motor unit action potentials (MUAPs) from electromyographic (EMG) signals (also known as EMG decomposition) is an important step in investigations aiming to obtain information on control strategies of the neuromuscular system and its state. For instance, the analysis of the shape of MUAPs and their frequency of occurrence may be used as an additional tool in the detection of some neuromuscular disorders. Although MUAPs can be manually extracted from the EMG, such a procedure is often time consuming and prone to error. In this context, systems which aim to automate the extraction of MUAPs play an important role. First, they allow for the reduction in the processing time of signals, and secondly, they introduce consistency across analyses. In this work, we present an automatic system for the extraction of MUAPs based on generative topographic mapping (GTM), which is a recently developed technique for data clustering and visualization. The system is composed of several signal processing units, including signal filtering and detection, feature selection, data clustering and visualization. Its input is a time-series, representing EMG activity, and its output is the visualization of MUAPs obtained through GTM. The performance of the system was assessed via the analysis of synthetic and experimental EMG signals, detected by means of concentric needle and surface electrodes, collected from healthy subjects executing muscle contractions with distinct levels of force. Our results show that the system is capable of accurately extracting MUAPs from the EMG.     

Identification of analytic signals

This paper is devoted to the identification of analytic signals and to find a solution to the following problem. Given a realization of an analytic signal, it is necessary to find the analytic function by which the signal is described. The proposed approach to this problem is based on relatively simple relationships existing between many analytic signals and their respective derivatives. These relationships are closely related to the properties of the dynamic systems which generate the signals under investigation. Simple identification procedures are described and tested by means of computer simulation.     

On the existence and the magnitude of electronic charges

In order to quantize Dirac's classical point electron¹ we supplement Einstein's classical equation (E/c)² ? p² = b2 with a reciprocal classical equation (CΔt)² ? (Δr)² = a² where b = mc and a is Dirac's signal radius. Δt is the time saved by a light signal in various states of motion of the electron, and a/c is the rest time saved. Our former efforts² of obtaining an integral equation for the probability amplitude have been rectified by Born.³ There is no solution of the integral equation, however, unless advanced and retarded phases are introduced simultaneously, along with Dirac's advanced and retarded potentials. We have obtained a transcendental equation for the eigen-value μ = αγ where α is the Sommerfeld fine-structure constant, and γ is the numerical factor in Dirac's signal radius a = γe²/mc². The smallest eigen-value is μ = 0.0299.That is, ab = hγ = h/210.     

The reconstruction of bordered- diagonal and Jacobi matrices from spectral data

Simple, new, direct methods are derived for constructing real, symmetric, bordered-diagonal and tridiagonal matrices from their eigenvalues and the eigenvalues of any one of their principal submatrices. A direct method is also presented for constructing, from its eigenvalues, a real tridiagonal matrix which is symmetric about both its main and secondary diagonals. The techniques described make use of special properties of positive, real, odd, rational functions which occur in electric circuit theory. Examples are given which demonstrate the various methods.