基于对星座图分形的Qam信号识别

星座图是Qam调制信号的重要特征，分形理论是研究图形属性的一种前沿工具。将分形和星座图结合，计算星座图所对应的格形分形维数和信息维数等分形理论中的特征量，把他们作为区分调制类别的特征向量，进行信号识别。该方法经实验验证能够有效的进行Qam信号的识别。     

语音信号非线性分析与处理

介绍基于混沌理论的语音信号非线性分析和处理。概括语音信号非线性和混沌的依据;描述了语音信号混沌特性参量,包括Ｌｙａｐｕｎｏｖ指数和分形维;讨论运用Ｔａｋｅｎｓ嵌入定理于语音信号相空间重构时的研究议题,包括嵌入维数、时间延迟、等;最后阐述应用ＲＢＦ神经网络进行基于混沌的语音信号非线性处理。     

基于小波变换与分形的中药指纹图谱的特征提取

探讨基于小波变换与分形的中药指纹图谱特征提取方法。使用小波变换将中药指纹图谱分解至不同的分辨尺度,然后利用分形理论计算各尺度下的分量的分形维数,用分形维数参量代替指纹图谱的采样值,对中药进行分析识别。试验结果表明,使用小波基分形参量对一药物指纹图谱的实验条件的辨别效果要优于单纯使用分形维数和使用指纹图谱的采样值。     

雷达辐射源信号脉内特征分析

脉内特征提取是新型雷达辐射源信号识别的关键问题。本文提出一种新的雷达辐射源信号脉内特征提取和识别方法．将雷达辐射源脉冲信号的分形维数作为识别脉内调制方式的分类特征,这些特征包含了雷达辐射源信号幅度、频率和相位等的变化和分布信息,反映了雷达辐射源信号脉内调制规律,理论分析和仿真实验结果都证明了这些特征具有对噪声不敏感的良好特性．通过10种典型雷达辐射源信号的特征提取和分类识别的实验结果表明,本文所提取的脉内特征类间距离大、类内距离小、正确识别率高．证实了本文方法的有效性。     

分形技术在轴承故障诊断中的应用

针对滚动轴承振动信号的特点,从分形原理出发,利用分形维数的概念,对由滚动轴承故障产生的非平稳、非线性信号进行了分形特征的定量描述。试验结果表明,由于滚动轴承不同故障动力学产生的机制不同,其分形维数明显不同。因此利用分形维数可以准确地诊断出滚动轴承的工作状态。     

基于分形理论的太赫兹光谱识别

介绍了分形的基本概念和分形盒维算法.提出了一种新的太赫兹光谱识别方法.实验中测得了两种中药的太赫兹光谱,算出了它们的盒维数并进行了比较.通过这种方法使不同的药品得到了很好的鉴别.     

基于分形维与缝隙参数的海杂波目标检测

针对分数布朗运动模型在不同尺度上粗糙度相同的缺陷,提出一种将高阶分形特征作为分形维数补充的目标检测算法。该方法将Hurst指数和缝隙特征相结合,分析比较了海杂波和目标的特性。在此基础上,对IPIX雷达实测数据进行实验分析。结果表明,对海杂波背景下的小目标检测,提出的算法比仅基于分形维数的检测算法性能更优。     

Locating the eye in human face images using fractal dimensions

Facial feature extraction is an important step in many applications such as human face recognition, video conferencing, surveillance systems, human computer interfacing etc. The eye is the most important facial feature. A reliable and fast method for locating the eye pairs in an image is vital to many practical applications. A new method for locating eye pairs based on valley field detection and measurement of fractal dimensions is proposed. Possible eye candidates in an image with a complex background are identified by valley field detection. The eye candidates are then grouped to form eye pairs if their local properties for eyes are satisfied. Two eyes are matched if they have similar roughness and orientation as represented by fractal dimensions. A modified approach to estimating fractal dimensions that is less sensitive to lighting conditions and provides information about the orientation of an image under consideration is proposed. Possible eye pairs are further verified by comparing the fractal dimensions of the eye-pair window and the corresponding face region with the respective means of the fractal dimensions of the eye-pair windows and the face regions. The means of the fractal dimensions are obtained based on a number of facial images in a database. Experiments have shown that this approach is fast and reliable     

Systems concept and components of fractal radio electronics: Part I. Development stages and the state of the art

A systemization is performed for the results of theoretical and experimental investigations that were obtained in radio physics and radio engineering with the help of fractal theory and the mathematical theory of fractional dimension and fractional operators with consideration for the scaling effects of real radio signals and electromagnetic fields. Classification and the analysis and synthesis methods of the components of fractal radio electronics (resistive-capacitive components with distributed parameters) with prescribed frequency characteristics, as well as the fields of application of such components, are considered. It is shown that non-linear, parametric, and other properties of simulated objects can be considered with the use of vectors of electrophysical parameters of layers and design parameters. New promising design versions of components with fractal dimensions, namely, fractal impedances, which can be used in various devices of fractal radio electronics, are proposed.     

一种分析稠密随机媒质的新方法

一种基于ＦＤＴＤ法的数值方法用来分析稠密离散随机媒质。本文采用在ＦＤＴＤ法的差分多格中进行随横填充来模拟随机媒质，并求解其瞬态电磁散射场。然后对该散射场曲线的分形维数进行了计算，数值结果表明，稠密离散随机媒质的瞬态散射场的分数数与其数密度之间作一定的范围内存在线性函数关系。     

Performance analysis of a rate adaptive multi-band ultra-wideband system based on quadrature fractal modulation scheme

1 Introduction Wornell and Oppenheim[1,2] first proposed a modulation technique as an interesting potential application of dy-homogeneous signals. Due to the fractal properties of the homogeneous signals, this technique is called fractal modulation afterwards. This class of homogeneous signals remains invariant under scaling of the time axis. Dy-homogeneous signals satisfy the dyadic self-similarity property[3] s (t ) = 2 kH s (2 kt) (1) For all integers k and a constant H, termed the degree…     

Estimating effective degrees of freedom in motor systems.

Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are the most popular. However, many biological data (or realistic experimental data) may be better represented by nonlinear sets than linear subspaces. We evaluate the performance of PCA and compare it to two nonlinear algorithms [Isomap and our novel pointwise dimension estimation (PD-E)] using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that PCA can lead to more accurate dimension estimates when considering additional properties of the PCA residuals, instead of the dominant method of using a threshold of variance captured. In contrast to the single integer dimension estimates of PCA and Isomap, PD-E provides a distribution and range of estimates of fractal dimension that identify the heterogeneous geometric structure in the experimental data. A strength of the PD-E method is that it associates a distribution of dimensions to the data. Since there is no a priori reason to assume that the sets of interest have a single dimension, these distributions incorporate more information than a single summary statistic. Our preliminary findings suggest that fewer than ten DOFs are involved in some hand motion tasks. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. Given the complex nature of experimental and biological data, we conclude that it is necessary and feasible to complement PCA with methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their DOFs.     

Optimal and robust memoryless discrimination from dependentobservations

Discrimination is considered between two possible sources based on dependent observations of their output. The discrimination problem is modeled by means of a general binary hypothesis test, the main emphasis being on situations that cannot be modeled as signals in additive noise. The observations are modeled as stationary m-dependent or ρ-mixing processes. The structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic, which is then compared to a threshold. Only fixed sample size tests are considered. Four different performance measures, which resemble the signal-to-noise ratios encountered in the signal in additive noise problems, are derived under different problem formulations. The optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations. For three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations. Computer simulation results that demonstrate the advantage of using these nonlinearities over the i.i.d. nonlinearity under the probability of error criterion are presented     

Locally optimum distributed detection of correlated random signalsbased on ranks

Distributed signal detection schemes have received significant attention, but most research has focused on cases where the observations at the different sensors are independent and the statistical model for the observations is completely known. If the observations at the different sensors consist of noisy versions of random signals which were produced by the same source, then these observations may not be independent. It is also possible that the noise distribution may not be completely known. Cases where weak random signals are observed in possibly non-Gaussian additive noise are considered. The focus is on cases where the sensor tests are based only on the ranks and signs of the observations. Numerical results are provided which indicate that distributed schemes based on ranks and signs are less sensitive to the exact noise statistics when compared to optimum schemes based directly on the observations. This is especially true for some cases where the actual noise distribution has heavy tails, which can cause the optimum schemes based directly on the observations to perform poorly. Analytical forms are given for the locally optimum sensor test statistics based on the ranks and signs of the observations, and we use these to find the best distributed detection schemes for some cases. In the course of obtaining our results, a general set of necessary conditions is given which provide the analytical forms of the locally optimum distributed sensor tests for cases where the observations are discrete random variables. Conditions of this type have not been given previously     

分形维数与光学小波变换

用光学方法成功地进行了分形图像的小工测出其分形维数。分形维数值的测定可以推动分形动力学的研究与发展。实验证明,光学小波变换不失为一种实时分析分形图像的重要方法。     

Resolution limits in signal recovery

Resolution analysis for the problem of signal recovery from finitely many linear measurements is the subject of this paper. The classical Rayleigh limit serves only as a lower bound on resolution since it does not assume any recovery strategy and is based only on observed data. We show that details finer than the Rayleigh limit can be recovered by simple linear processing that incorporates prior information. We first define a measure of resolution based on allowable levels of error that is more appropriate for current signal recovery strategies than the Rayleigh definition. In the practical situation in which only finitely many noisy observations are available, we have to restrict the class of signals in order to make the resolution measure meaningful. We consider the set of bandlimited and essentially timelimited signals since it describes most signals encountered in practice. For this set, we show how to precompute resolution limits from knowledge of measurement functionals, signal-to-noise ratio, passband, energy concentration regions, energy concentration factor, and a prescribed level of error tolerance. In the process, we also derive an algorithm for high-resolution signal recovery. We illustrate the results with examples in one and two dimensions     

Fractal geometry of the surface potential in electrochemically deposited platinum and palladium films

The surface potentials are distributed very nonuniformly in electrochemically deposited thin films of palladium and platinum, and it reflects the grain structure of their surface profile. The Hausdorf-Bezikovich space dimensions of the surface potentials in these films much exceed the topological dimension of their projections, which is indicative of their fractal geometry. It is found that the surfaces of platinum and palladium films differ both in the spread of magnitudes of the surface-potential nonuniformities and in the shape and character of their distribution. This substantially affects the way of formation (geometry) of their potential profile and the values of their fractal dimensions. In addition, the fractal geometry of the potential profile of these film surfaces leads to the fact that the total electric charge of their surfaces varies much slower-it is proportional to the change in their linear dimensions to power (4 ? D _f), where 2 < D _f < 3, instead of being proportional to the square of the change in the linear dimensions of the areas under investigation as in the two-dimension case. As a result, it is shown that, for the accurate designing of devices with metal components of submicrometer and nanometer sizes on the basis of thin films of platinum and palladium, it is necessary to take into account their fractal geometry.     

基于小波和分形理论的调制信号特征提取方法研究

本文针对通信信号这种非平稳的、信噪比(SNR)变化范围较大的信号,应用小波分析和分形理论,提出了有效的特征提取方法,所提取的分形特征包含了区别不同调制类型所需的幅度、频率和相位等主要信息。同时这种特征具有较好的抗干扰特性,基于这种特征的分类器的设计简单、高效。计算机模拟结果表明此方法的有效性。     

Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition

Fractal dimension measures the geometrical complexity of images. Lacunarity being a measure of spatial heterogeneity can be used to differentiate between images that have similar fractal dimensions but different appearances. This paper presents a method to combine fractal dimension (FD) and lacunarity for better texture recognition. For the estimation of the fractal dimension an improved algorithm is presented. This algorithm uses new box-counting measure based on the statistical distribution of the gray levels of the “boxes”. Also for the lacunarity estimation, new and faster gliding-box method is proposed, which utilizes summed area tables and Levenberg-Marquardt method. Methods are tested using Brodatz texture database (complete set), a subset of the Oulu rotation invariant texture database (Brodatz subset), and UIUC texture database (partial). Results from the tests showed that combining fractal dimension and lacunarity can improve recognition of textures.     

真实孔径雷达海洋图像的分形特征分析

结合海洋雷达图像的电磁散射机理,采用小波分析方法对真实孔径雷达海洋图像的分形维数和特征进行分析,发现虽然海洋表面波具有分形的特征,但是海洋雷达图像在布拉格散射机制主导的情况下,不具备分形特征.为了准确计算雷达图像的分形维数,还对差分盒计数法、数学形态学方法和小波分析方法三种分形维数的计算方法进行了评估,通过对已知维数的模拟图像进行分形维数的计算,分析了三种方法的优缺点.