Systems with infinite-dimensional state space: The Hilbert space approach

The control of infinite-dimensional systems has received much attention from engineers and even mathematicians. Realizability although first considered in [4] has been ignored until recently. Ironically enough while state-space systems theory was developing in the early 1960's a mathematical study of scattering and of non-self-adjoint operators produced a parallel theory which was infinite dimensional from the beginning. When the close relationship between the two subjects became known time invariant infinite-dimensional systems theory advanced quickly and at a general level it now seems reasonably complete. This paper describes the connection between mathematical scattering and systems. It then gives a thorough treatment of infinite-dimensional time invariant continuous time systems. The last section lists recent scattering results which might be of engineering interest.     

DIGITAL PROCESSING OF THE POLARIZATION STATE OF GEOPHYSICAL ULF SIGNALS

In this paper, the evaluation by running window smoothing is used for the digital processing of the polarization of geophysical ULF signals. The observed signals are resolved into two orthogonal complex components so that it is no longer necessary to consider the phase and amplitude of the signals simultaneously.     

Reconstruction of aperiodic FRI signals and estimation of the rate of innovation based on the state space method

In the absence of observation noise, it is known that it is possible to develop exact sampling schemes for a large class of parametric non-bandlimited signals, namely, certain signals of finite rate of innovation (FRI signals), either periodic or aperiodic, such as streams of Diracs, nonuniform splines or piecewise polynomials. A common feature of such signals is that they have a finite number of degrees of freedom per unit of time and they can be reconstructed from a finite number of uniform samples of the filtered signal. Unfortunately, the accuracy of such reconstruction substantially degrades when the samples are distorted by noise. For the case of periodic FRI signals, good algorithms based on the state space method have been proposed which are robust against noise. However, in the case of aperiodic signals, these algorithms may still fail to accurately reconstruct the signals due to ill-conditioning problems that often arise in the matrices involved. This paper proposes a new reconstruction method for aperiodic FRI signals that is also based on the state space method but has a considerably better numerical conditioning than previous reconstruction algorithms. This advantage is achieved by using a frequency domain formulation.     

基于Wigner分布的脑电信号处理

临床实践表明,脑电信号中包含有大量的生理与疾病信息。对脑电信号进行行之有效的处理,不仅可以为医生提供临床诊断信息,而且可以为某些脑疾病的治疗提供有效的治疗手段。目前,随着信号处理技术的发展,在脑电信号处理中已应用了多种信号分析方法来提取脑电信号中所包含的信息,但大多数还是停留在理论研究阶段。本文在研制虚拟式脑电图仪的过程中,考虑到Wigner分布在各种时频分布中具有最简单的形式和良好的性质,从临床应用及医学研究相结合的角度出发,应用Wigner分布对脑电信号进行时频分析以提取脑电信号中的特征信息。对实测脑电数据的分析表明,应用此方法可获得较好的分析效果。     

Spotlight SAR data focusing based on a two-step processing approach

The authors present a new spotlight SAR data-focusing algorithm based on a two-step processing strategy that combines the advantages of two commonly adopted processing approaches: the efficiency of SPECAN algorithms and the precision of stripmap focusing techniques. The first step of the proposed algorithm implements a linear and space-invariant azimuth filtering that is carried out via a deramping-based technique representing a simplified version of the SPECAN approach. This operation allows the authors to perform a bulk azimuth raw data compression and to achieve a pixel spacing smaller than (or equal to) the expected azimuth resolution of the fully focused image. Thus, the azimuth spectral folding phenomenon, typically affecting the spotlight data, is overcome, and the space-variant characteristics of the stripmap system transfer function are preserved. Accordingly, the residual and precise focusing of the SAR data is achieved by applying a conventional stripmap processing procedure requiring a minor modification and implemented in the frequency domain. The extension of the proposed technique to the case of high bandwidth transmitted chirp signals is also discussed. Experiments carried out on real and simulated data confirm the validity of the presented approach, which is mainly focused on spaceborne systems     

Model based phase unwrapping of 2-D signals

A parametric model and a corresponding parameter estimation algorithm for unwrapping 2-D phase functions are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model fitting, the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise, as well as to local errors. In its first step, the algorithm fits a 2-D polynomial model to the observed phase. The estimated phase is then. Used as a reference information that directs the actual phase unwrapping process. The phase of each sample of the observed field is unwrapped by increasing (decreasing) it by the multiple of 2π, which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate. In practical applications, the entire phase function cannot be approximated by a single 2-D polynomial model. Hence, the observed field is segmented, and each segment is fit with its own model. Once the phase model of the observed field has been estimated, we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model field     

基于图像处理技术的雷达辐射源信号时频特性分析

针对常用时频分析方法对多分量雷达辐射源信号(RES)分析和处理的不足,提出一种基于图像处理技术的多分量RES时频特性分析方法.该方法通过时频分布图的平滑滤波、阈值处理和基于形态学细化等算法来提取RES自分量,在有效抑制噪声的同时,能够得到具有高分辨率的多分量RES时频图.仿真实验表明,该方法既克服了常用时频分析方法的不足,又优于时频重排方法对多分量RES的时频特性分析.     

基于有限状态机的雷达状态模型建立

现代雷达具有功能多特点.针对雷达系统控制,采用传统程序设计方法存在调试周期长,可移植性和可扩展性差的特点.本文采用有限状态机理论对雷达状态进行模型建立,根据状态机理论,通过仿真建立相应的状态切换模型,工程实践表明有限状态机能较好的进行雷达系统控制设计,系统可扩展性、可移植性较好.     

S-Vivaldi：一种基于空间修复的因特网时延空间嵌入算法

为减少违反三角形不等式(TIV)对因特网时延空间建模的影响,提出了一种基于空间修复的因特网时延空间嵌入算法S-Vivaldi。S-Vivaldi先对原有的时延空间D进行指数变换修复,获得一个几乎没有TIV的距离矩阵D’,再对D’采用Vivaldi算法进行坐标嵌入,当需要预测任意2个节点间的时延时,再进行一系列的逆变换。实验表明,该算法在大多数情况下可以显著提高预测精度。     

信号在多尺度空间的滤波

本文从多分辨率分析出发,结合离散正交小波变换（ＤＷＴ）的理论,提出了一种在保护信号边缘的前提下有效去除脉冲噪声的方法,该方法通过对各尺度下的未抽取前的小波系数进行非线性滤波处理,达到了在保护信号边缘的同时,有效去除白噪声及脉冲噪声的目的。并用实验结果进行了验证。     

基于状态空间法的非理想Boost电路开环建模

Boost变换器是组成高阶变换器的基本单元,故对其建模和仿真的研究有着理论和实际意义。状态空间平均法是DC-DC变换器建模的有力工具。在考虑了电感电容高频寄生电阻的条件下,应用状态空间平均法对非理想Boost变换器进行建模。为统一开关变换器不同工作状态下的状态方程,在此引入开关函数。开关函数的引入使得对状态方程平均化的问题转化为对开关函数平均化的问题,简化了建模过程,且平均化的开关函数具有明确的物理意义。最后将数学模型与电路模型的仿真结果以及实测数据加以对比,得出了较为一致的结论,为直流变换器的设计和分析提供参考。     

A state space approach to the design of globally optimal FIR energycompaction filters

We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter F_opt(z)=H_opt(Z)H_opt (z^-1) corresponding to the compaction filter H_opt (z). By expressing F(z) in the form D(z)+D(z^-1), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the causal function D(z). For a given input power spectrum, the resulting filter F_opt(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining H_opt(z) from F_opt(z) does not require an additional spectral factorization step. The minimum-phase spectral factor H_min(z) can be obtained automatically by relating the state space realization of D_opt(z) to that of H _opt(z)     

Bernoulli operator: a low-level approach to log-domain processing

A low-level large-signal continuous-time operator, governed by the Bernoulli nonlinear differential equation is proposed. This cell consists of a suitably biased bipolar junction transistor and an emitter-connected grounded capacitor, and is shown to formalise in a convenient manner, with signal-processing in the log-domain     

Smoothing of discontinuous signals: the competitive approach

Discontinuous signals buried in noise cannot be recovered by linear filtering methods. This paper presents a new class of nonlinear filters in which sets of forward and backward linear predictors and smoothers compete with each other at each timestep. The winner of each competition is granted the right to produce the smoothed estimate at that timestep. This conceptually simple approach to nonlinear filtering, called the competitive smoothing approach, is justified by considering sets of Kalman filters (corresponding to the hypotheses used in the Bayesian framework) which are used to derive model credibility coefficients. These are shown to essentially “switch” between the various models. We argue that the concept of competitive smoothing is considerably more general than just the Kalman setting, and can be used with almost any predictors and/or smoothers. Several examples are presented which demonstrate the efficacy of the approach at both smoothing and preserving jump discontinuities. Comparisons are made with the other main nonlinear filtering approach, the median filter     

Sampling and processing of color signals

Digital signal processing tools are used to determine the proper sampling of color spectra and the effect of sampling on the accuracy of derived properties such as CIE tristimulus values and color rendering indexes. It is found that 10 nm sampling is adequate for most applications, but not for more exacting textile and paint matching applications. Special methods are proposed to treat the cases of color signals with delta function components such as fluorescent lights.