The coherent digital processing of the output signal of the Snail gravitational antenna

The statistical problem of the synthesis of a digital processing algorithm for the output signal of the Snail resonant gravitational antenna by analog prototype is considered. The discretization step in the ADC-DAC system is selected on the basis of the Kotelnikov theorem (a sampling theorem) for quasi-harmonic signals.     

Signal reconstruction from the undersampled signal samples

It is well-known from the celebrated Shannon sampling theorem for bandlimited signals that if the sampling rate is below the Nyquist rate, aliasing takes place and the original signal cannot be reconstructed back by simply passing the signal samples through an ideal lowpass filter. However, researchers such as Stern and Gori have shown the existence of some classes of signals for which the signals are sampled below the Nyquist rate but perfect signal reconstruction is still possible from the given signal samples. Here, we present a generalized lowpass sampling theorem and show that Stern’s and Gori’s lowpass sampling theorems are special cases of it. A sampling theorem for the bandpass signals in the linear canonical transform domains is also presented and its special cases are discussed. Using a modification of the conventional natural sampling waveform with a specific width of the pulses, it is shown that the sampling rate in our generalized lowpass sampling theorem and hence in the Stern’s and the classical Shannon sampling theorems can be further reduced by a factor of two, while for the bandpass signals, the reduction in the sampling rate by some factor is possible only under some restricted conditions.     

Formulation of the Shannon theorem for a discrete noisy channel

In this paper, the Shannon theorem is formulated for a discrete noisy channel in terms used in the Shannon formulation. Proof of the theorem is based on the theory of optimal signals reception, in which the signal intensity with respect to noise has a significant meaning. Although the formulation contains the notions of the channel capacity and the message-source entropy, it substantially differs from the Shannon formulation. The obtained formulation allows us to explain some cases where the information transmission conditions do not satisfy the Shannon theorem.     

Accuracy of Determining Reverberation Parameters during Recovery of a Signal with Reverberation Distortions in the Case of Discrete Delays

We discuss the accuracy of determining reverberation parameters, which is required to recover a signal with reverberation distortions. It is shown that if the signal with distortions is digitized under conditions of the sampling theorem, then it is insufficient to determine the delay time of the retarded signal with an accuracy of the sampling interval. We present an iterative algorithm for determining the reverberation parameters with sufficient accuracy.     

New convolution theorem for the linear canonical transform and its translation invariance property

The linear canonical transform (LCT), which is a generalization of the Fourier transform (FT), has many applications in several areas, including signal processing and optics. Many properties for this transform are already known, but an extension of convolution theorem of FT is still not having a widely accepted closed form expression. In the literature of recent past different authors have tried to formulate convolution theorem for LCT, but none have received acclamation because their definition do not generalize very nicely the classical result for the FT. Moreover, those definitions exhibit only partial invariance properties which prevent their actual use in many applications of signal processing. The purpose of this paper is to introduce a new convolution structure for the LCT that preserves the translation invariance property. Indeed, an effective translation invariance is obtained by slightly modifying the former definitions and by introducing linear canonical translation operators.     

A Sound Field Separation and Reconstruction Technique Based on Reciprocity Theorem and Fourier Transform

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.     

基于中国余数定理的欠采样下余弦信号的频率估计

基于中国余数定理的重构算法的信号频率估计是近年来信号处理、电磁学以及光学等领域的前沿问题,但目前这些研究仅限于对复指数信号做粗略频率估计.因而,本文把基于中国余数定理的频率估计从复指数信号粗估计拓展到实余弦信号精细估计领域,其所提出的估计方案处理过程如下:1)对高频余弦波形进行过零点检测,确定信号的相位信息;2)对各路欠采样信号做快速傅里叶变换,并借助Candan估计器对各路谱峰值做频率校正以获取高精度余数估计,基于此算出频偏值以做相位校正;3)用提出的基于相位特征分类方法对校正得到的余数做筛选;4)将筛选出的频率余数代入闭合形式的中国余数定理得到原信号频率的高精度估计.此外,本文还推导出了频率估计方差的理论表达式.数据模拟实验验证了该表达式的正确性,实验结果还反映了本文提出的方案具有高精度和高抗噪性能.     

Generalized Noether's theorem. I. theory

This article is a theoretical investigation of generalized Noether's theorem, which, though unconcerned with considerations such as coordinate transformations, symmetry, and invariance, is the basic mechanism of conventional Noether's theorem, its extensions, and its inverse. The generalized theorem is a completely new approach to the subject—formally, conceptually, and practically. It is an association, for a set of field equations, of field variations with conserved currents. The theorem is stated from two points of view and analyzed with regard to its interpretation and its formal and conceptual relation to conventional Noether's theorem and extensions, transformation groups, and Hamilton's principle. The inverse theorem is also treated. The role of coordinate transformations in conventional Noether's theorem is analyzed.     

一种用于红外目标信号接收的稳健匹配滤波算法

针对远距离红外探测目标信号的不确定性问题,提出一种稳健的红外信号匹配滤波新算法.定性分析了红外探测目标的有用信号谱畸变来源,基于巴什瓦定理建立了目标信号的不确定谱模型,并分析了信号谱畸变的相关因子.利用极大极小方法构建稳健匹配滤波的信噪比输出鞍点解,并基于内层极大和外层极小的二层遗传优化算法求解鞍点解和最不利信号频谱,...     

Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. This paper addresses the problem of signal reconstruction from multichannel and periodic nonuniform samples in the LCT domain. Firstly, the multichannel sampling theorem (MST) for band-limited signals with the LCT is proposed based on multichannel system equations, which is the generalization of the well-known sampling theorem for the LCT. We consider the problem of reconstructing the signal from its samples which are acquired using a multichannel sampling scheme. For this purpose, we propose two alternatives. The first scheme is based on the conventional Fourier series and inverse LCT operation. The second is based on the conventional Fourier series and inverse Fourier transform (FT) operation. Moreover, the classical Papoulis MST in FT domain is shown to be special case of the achieved results. Since the periodic nonuniformly sampled signal in the LCT has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived MST and the specific space-shifting property of the LCT. Last, the potential applications of the MST are presented to show the advantage of the theory.     

Oscillatory free induction decay in angular distribution of nuclear radiation

A theoretical consideration of the free induction decay (FID) signal formation in the angular distribution of radiation, emitted by oriented nuclei after excitation by a long radiofrequency resonance pulse t_p ? T¹₂, is carried out. The well-known theorem on the oscillatory FID signal is expanded for the case of second rank tensors.     

Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach

The heartbeat rate signal provides an invaluable means of assessing the sympathetic-parasympathetic balance of the human autonomic nervous system and thus represents an ideal diagnostic mechanism for detecting a variety of disorders such as epilepsy, cardiac disease and so forth. The current study analyses the dynamics of the heartbeat rate signal of known epilepsy sufferers in order to obtain a detailed understanding of the heart rate pattern during a seizure event. In the proposed approach, the ECG signals are converted into heartbeat rate signals and the embedology theorem is then used to construct the corresponding multidimensional phase space. The dynamics of the heartbeat rate signal are then analyzed before, during and after an epileptic seizure by examining the maximum Lyapunov exponent and the correlation dimension of the attractors in the reconstructed phase space. In general, the results reveal that the heartbeat rate signal transits from an aperiodic, highly-complex behaviour before an epileptic seizure to a low dimensional chaotic motion during the seizure event. Following the seizure, the signal trajectories return to a highly-complex state, and the complex signal patterns associated with normal physiological conditions reappear.     

Multichannel sampling expansion in the linear canonical transform domain and its application to superresolution

The linear canonical transform (LCT) describes the effect of first-order quadratic phase optical system on a wave field. In this paper, we address the problem of signal reconstruction from multichannel samples in the LCT domain based on a new convolution theorem. Firstly, a new convolution structure is proposed for the LCT, which states that a modified ordinary convolution in the time domain is equivalent to a simple multiplication operation for LCT and Fourier transform (FT). Moreover, it is expressible by a one dimensional integral and easy to implement in the designing of filters. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, a practical multichannel sampling expansion for band limited signal with the LCT is introduced. This sampling expansion which is constructed by the new convolution structure can reduce the effect of spectral leakage and is easy to implement. Last, the potential application of the multichannel sampling is presented to show the advantage of the theory. Especially, the application of multichannel sampling in the context of the image superresolution is also discussed. The simulation results of superresolution are also presented.     

Minimum signals in classical physics

The bandwidth theorem for Fourier analysis on any time-dependent classical signal is shown using the operator approeoch to quantum mechanics. Following discussions about squeezed states in quantum optics, the problem of minimum signals presented by a single quantity and its squeezing is proposed. It is generally proved that all such minimum signals, squeezed or not, must be real Gaussian functions of time.     

Probing the spin state of a single electron trap by random telegraph signal

We have studied the random telegraph signal (RTS) generated by a single paramagnetic spin center adjacent to a submicrometer silicon metal-oxide-semiconductor field-effect transistor. An in-plane magnetic field induces a substantial change in the statistics of the RTS. We show that a model using the grand partition theorem can qualitatively explain the change in statistics of the RTS as a function of the applied magnetic field. While the data at high temperatures can be well described by this simple model, quantitative discrepancy increases as the temperature is lowered.     

条干均匀度仪波谱图算法设计与实现

条干均匀度仪的波谱图能够精确的反映出纱疵的周期性特征,从而可以快速地确定出纺纱工艺流程中故障的位置,但是将波谱图快速准确的实现是研究的难点。本文基于数字信号处理中的重采样定理,通过对不同机械故障所产生的纱线信号进行分析,改进了条干均匀度仪波谱图算法,该算法在需要观测的波长范围内构建了110个不同频带的带通滤波器,根据相邻滤波器频带关系分组进行波谱分析。通过DSP28335微处理器的数据采集、信号处理和上位机波谱图显示的系统进行实验,结果证明了该算法的可行性。其改进后的算法极大的减小了以往所用硬件的复杂度、提高了运算速度并增加了波谱图的可观测范围,且能够更精确的检测出故障位置。     

Principal component analysis for emergent acoustic signal detection with supporting simulation results

A method is introduced that uses principal component analysis (PCA) to detect emergent acoustic signals. Emergent signal detection is frequently used in radar applications to detect signals of interest in background clutter and in cognitive radio to detect the primary user in a frequency band. The method presented differs from other standard techniques in that the detection of the signal of interest is accomplished by detecting a change in the covariance between two channels of data instead of detecting the change in statistics of a single channel of data. For this paper, PCA is able to detect emergent acoustic signals by detecting when there is a change in the eigenvalue subspace of the covariance matrix caused by the addition of the signal of interest. The algorithm's performance is compared to an energy detector and the Neyman-Pearson theorem. Acoustic simulations were used to verify the performance of the algorithm. Simulations were also used to examine the effectiveness of the algorithm under various signal-to-interferer and signal-to-noise ratios, and using various test signals.     

混沌Lur’e系统的线性输出反馈同步

针对一类特殊的混沌Lur’e系统,以系统最后一状态变量作为驱动信号进行误差的线性输出反馈,提出一个同步的全局控制规律,并证明了同步的渐近稳定性.最后以蔡氏振子为例进行仿真,验证该同步方法的有效性. 关键词： 混沌同步 输出反馈 Lur’e系统 蔡氏振子     

Generalized Noether's theorem. II. Application

We consider the application of generalized Noether's theorem, a completely new approach — formally, conceptually, and practically — to Noether's theorem, its extensions, and its inverse. We discuss application in general and present specific applications: to the Dirac field, to creation/annihilation currents, and to zilch.