面向数据挖掘的时间序列符号化方法研究

针对时间序列的数据挖掘首先需要将时间序列（Ｔｉｍｅ Ｓｅｒｉｅｓ）数据转换为离散的符号序列（Ｓｙｍｂｏｌ Ｓｅｑｕｅｎｃｅｓ）,本文提出了一个简单高效的时间我符号化方法,该方法的特点：一是利用线性化分段表示法所独有的形态分割与表达能力实现了时间序列的分段与表示：二是利用神经网络模糊聚类算法实现了时间序列的在线聚类。提出以矢量间开矿相似性度量作为聚类依据。并利用该方法实现了对金融领域时间序列数据的符     

Interpolation of band-limited functions using the approximate prolate series (Corresp.)

A new series for the interpolation of band-limited functions is found by using an approximation to tho prolate spheroidal wave function as a convergence factor. A truncation error bound is found for the central interpolation of band-limited functions using the new series. It is shown that this bound is lower than other known bounds in many cases of interest.     

Infinite series representations of the bivariate Rayleigh andNakagami-m distributions

Despite the usefulness of the bivariate (correlated) Nakagami-m cumulative distribution function (cdf) in communications systems analysis, an infinite series for the computation of this function is not known. In this letter, an infinite series representation of the bivariate cdf is derived. Bounds on the error resulting from truncation of the infinite series are also derived     

Analysis of coupled nonuniform transmission lines using Taylor's series expansion

A new method is introduced for the frequency domain analysis of arbitrarily loaded lossy and dispersive nonuniform coupled transmission lines. We assume that the per-unit-length matrices are known and can be expressed by a converged Taylor's series. All known per-unit-length matrices, as well as the voltages and currents, are expanded in Taylor's series. The solutions of voltages and currents are obtained after finding the unknown coefficients of the series. The validity of the method is verified using the analysis of some special kinds of coupled lines.     

On the spectral coherence of nonstationary processes

It is shown that for a single path of a nonstationary process, reliable (i.e., low-variance) measurements of the degree of coherence between two spectral bands with substantial separation must be smaller than 1/2 unless the nonstationarity is of a special type. That is, the nonstationarity must be either of a known form (prior to measurement) or of a periodic nature, which is known as cyclostationarity. It is concluded that spectral correlation measurements on single time series are of highly questionable value for detection and characterization of nonstationarity, except in the special cases of cyclostationarity     

On the Resolution Probability of MUSIC in Presence of Modeling Errors

The problem of resolving closely spaced signal sources using an antenna array remains a difficult one, although several estimation methods are available in the literature. When the array correlation matrix is known, the resolution capability of subspace algorithms is infinitely high. However, in the presence of modeling errors the resolution deteriorates, even for a known correlation matrix. In this paper, we analyze the MUSIC method, by way of three different definitions of the resolution. Assuming Gaussian circular random modeling errors, we determine the corresponding expressions of the probability of source resolution versus the model mismatch. A first series of simulations validates the mathematical expression of the three resolution probabilities. A second series of simulations is used to select among them the tightest one to the empirical one. The results are useful, e.g., for determining the necessary antenna calibration accuracy to achieve a target performance.     

On the Utility of Laguerre Series for the Envelope PDF in Multipath Fading Channels

It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases, we need to calculate the probability density function (pdf) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope pdf for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the pdf: a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error. This Laguerre series with a finite number of terms, which expresses the envelope pdf just in terms of simple polynomial–exponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small.      

A Convenient Multivariate Gram-Charlier Type A Series

It is often necessary to approximate the probability density function of a random variable from given statistical moments. The Gram-Charlier Type A series is one well known method for such representations. In this note, the Gram-Charlier Type A series is generalized to the multidimensional case.     

On the Subjective Evaluation of Protection-Ratios' Measurements for Co-Channel FM-TV Interference under Variable (S/N) Ratios

The relation between the image impairment grade and the ratio of wanted-to-interference, known as C/I power ratios, for FM co-channel television systems is studied. The variation of C/I ratio with picture impairment grade is investigated for different noise levels, through a series of experiments.     

一种新颖的混沌时间序列分析方法

本文提出了一种新颖的混沌时间序列分析方法,即从被加性高斯白噪声污染的混沌时间序列中估计其系统参数并同时进行噪声抑制的方法。假定产生混沌时间序列的模型已知,但相应的参数未知。这种新方法把对混沌时间序列的参数估计和噪声抑制看作是一种最小化过程,并利用了最速梯度下降方法解决。数值模拟实验表明新方法要优于现有的方法,是估计混沌系统系数和噪声抑制的一种有效的方法。     

The measurement of radiating pattern by using the cylindrical function

The paper proposes a new method of measuring radiating patterns from antennas or EMI sources. In this method, the cylindrical function is adopted for the near-to-far-field transformation. The new measuring method does not require the large free space prescribed by FCC and CISPR. The radiated electric field is described by using the series cylindrical function, i.e. the Hankel function, with unknown series coefficients. Applying the boundary condition on the virtual boundary, which surrounds the radiating objects in free space, the unknown series coefficients in the radiated field can be determined. Using asymptotic expansion of the Hankel function with the known series coefficients, the far-field data, that is the radiating patterns, are given. In order to verify the proposed method, numerical experiments are performed with a line sources array. The results show good agreement with the array antenna pattern equation. Moreover, two types of measurement systems are suggested for the radiating patterns, both employing a vector network analyser. Accurate radiating patterns can be measured with compact systems using the proposed method.     

非傍轴光束级数修正解的有效性

当光束具有较大的发散角或光束束腰可与波长相比拟时，傍轴近似不再成立。需要发展更为严格的非傍轴处理方法。迄今已提出许多方法．例如微扰法、级数展开法、算子法、角谱分析法和波动方程积分解等方法，用以研究光束的非傍轴传输行为。不同方法具有各自的优缺点和适用范围。分析了非傍轴光束级数解的有效性。对波动方程积分解和级数解作了详细的数值计算和比较，指出当ω0≤0．2251λ时(ω0为束腰宽度，λ为波长)，级数解对傍轴解有修正作用。但是，当ω0≤0．2251λ时，级数解会给出无意义的结果，并且会发散。级数解必须在其有效范围内使用。级数解的适用范围与光束的束腰宽度、传输距离以及所使用的级数解的阶次有关。     

Exponential parameter estimation an the presence of knowncomponents and noise

In the determination of the natural modes of an electromagnetic scatterer, the measured time series will contain desired information, noise, and quite often known transient components introduced by the excitation source or measuring equipment. This paper describes a linearly constrained total least squares (LCTLS)-Prony method for extracting the exponential model parameters from observed transient data. For such problems, the TLS criterion yields better parameter estimates than LS. Moreover, the incorporation of known signal information via constraints leads to even greater improvements in performance. Mathematical connections between LCTLS-Prony and a TLS variation of time series deflation (TSD) are used to derive constraints for higher order excitation poles. Also, we use TSD concepts to derive numerically superior data transformations For LCTLS. Simulation studies involving idealized test data and synthetic scattering response data of a perfectly conducting sphere demonstrate the advantages of the method     

矢量衍射理论的比较研究及标量近似的有效性

光束束腰与波长相比拟时,标量近似已不再成立.以高斯光束的微小圆孔衍射为例,对矢量衍射场的级数解、非傍轴近似解以及精确解进行了详细的数值计算和比较研究.结果表明,对受硬边光阑限制的非傍轴光束,级数展开法适用于处理光束在近场区域的传播,而非傍轴近似解则适用于处理非近场区域光束的传播,具有一定的互补性.讨论了高斯光束圆孔衍射标量近似的有效性,当高斯光束的束腰半径、衍射孔孔径大于几个光波波长时,标量衍射理论是精确、有效的.     

An asymptotic series for early time response in transient problems

An asymptotic series is described suitable for the evaluation of the early time response in a transient problem. Once the solution in the frequency domain is known in certain forms of ascending series of frequency (including optical, diffracted, and creeping waves), asymptotic formulas are developed to "translate" it readily into the time domain.     

Volterra series representation of a forward-biased p-i-n diode

A nonlinear model is proposed for a forward-biased p-in diode controlled by an ac signal consisting of a group of sinusoidal signals. The model is applicable to these phases of diode operation where linearized basic physical equations are valid. Current-voltage relations have been obtained for junctions and the "i" region in the form of a Taylor series with frequency-dependent coefficients. The new model is valid for signal levels considerably exceeding those admissible for the known linear model [3], [4]. A new form of signal limiting condition, suitable for measurement verification and calculations, has been obtained. The Volterra series for the equations representing the diode has been found which correspond to the Taylor series obtained. The convergency condition for this series is identical to that for thel Taylor series. The conformability of measurement and calculation results fully testifies to the usefulness of the proposed model for nonlinear distortion analysis.     

On the ergodic capacity of multi-hop wireless relaying systems

The ergodic capacity in Rayleigh fading of multihop wireless transmission systems employing either amplifyand- forward relaying or decode-and-forward relaying is studied, assuming channel state information is only known at the receiving terminals. Two upper bounds based on Jensen?s inequality and the harmonic-geometric means inequality as well as an infinite series representation for the ergodic capacity of an amplify-andforward multi-hop transmission system are derived. Numerical results are provided to examine the tightness of the upper bounds as well as to show the high accuracy of the infinite series approach. In addition, the ergodic capacity of a decodeand- forward multi-hop transmission system is obtained. It is shown that multi-hop transmission systems employing a decodeand- forward relaying scheme achieve higher ergodic capacities than multi-hop transmission systems with amplify-and-forward relaying schemes.     

A simple procedure to eliminate known poles from a time series

An extremely simple procedure is presented for eliminating known or previously computed poles from a time series and for obtaining a `deflated' time series which contains only the remaining poles. Time-series deflation can be used in combination with any numerical algorithm used to compute poles. As an important example, it is demonstrated how the time-series deflation technique combined with Prony's method can produce more accurate results than the use of Prony's method alone     

Variance bounds on the estimation of reflectivity and polarizationparameters in radar meteorology

Cramer-Rao lower bounds are presented on the estimation accuracy of any unbiased estimator of power and polarization parameters of echoes received by a meteorological radar. The analysis is carried out by using a widely accepted model for radar meteorology-the multivariate Gaussian model (Rayleigh fading)-along with the assumptions that the time series of horizontally and vertically polarized echoes are acquired simultaneously, that the autocorrelation function of the process is known, and that the signal-to-noise ratio (SNR) is high. Two significant results of this analysis are that the lower bounds are independent of the known autocorrelation function, and that the effective number of independent samples is always equal to the total number of samples. An explicit construction of maximum-likelihood estimators is also provided     

A simple method to approximate the probability of error for equal gain combiner over independent fading channels

Using the Beaulieu series, the probability of error for equal gain combiner over independent fading channels can be formulated in the form of an infinite series. The computation of the coefficients of this series needs complicated integrations over fading envelope distribution. In this paper, a new approximation method is developed for the computation of the required coefficients of the error probability series, which needs only mean and variance of the fading envelope. Hence, the purposed method eliminates the need for complicated integrations while computing the required coefficients. This feature provides an interesting flexibility for our developed method, so that it can be used as a unified method for performance analysis of equal gain combiner over various independent fading channels, especially where the required integrations have no closed‐form solutions. To present an application for the proposed approximation method, the fading channel is modeled by three‐parameter generalized Gamma distribution (GG3), which is a generic model that covers many well‐known channel models for both multipath and shadow fading. The presented numerical results show good accuracy as well as low computational complexity of the presented method. Copyright © 2007 John Wiley & Sons, Ltd.