Blind reconstruction of non-minimum-phase systems from 1-D obliqueslices of bispectrum

The author considers the problem of identifying a non-minimum-phase signal from one-dimensional slices of its output bispectra. It is proved that any single slice of the bispectrum carries sufficient information to estimate the impulse response of a complex valued system within a time shift, as long as the chosen slice is not parallel to any one of the frequency axes or to the diagonal at 135 degrees. The author also derives identifiability criteria associated with complex valued signals that admit finite-dimensional ARMA representations. One-dimensional techniques are proposed for signal reconstruction from bispectrum slices and their performance is investigated through Monte-Carlo simulations. The slices required for the proposed method can be estimated on a polar raster directly from observations, avoiding the heavy computational burden associated with cumulant estimates. The freedom to choose arbitrarily oriented and shifted slice(s) allows bispectrum regions dominated by larger estimation variance and higher noise to be avoided     

System reconstruction based on selected regions of discretizedhigher order spectra

We consider the problem of system reconstruction from arbitrarily selected slices of the nth-order output spectrum. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two one-dimensional (1-D) slices of the discretized nth-order output spectrum, (n⩾3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice suffices for system reconstruction. The ability to choose the slices to be used for reconstruction enables us to avoid regions of the nth-order spectrum, where the estimation variance is high, or where the ideal polyspectrum is expected to be zero, as is the case for bandlimited systems. We show that the obtained system estimates are asymptotically unbiased and consistent. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the proposed method over existing approaches in the case of bandlimited systems     

Narrowband weak signal detection by higher order spectrum

A study of narrowband weak signal detection by higher order spectrum (HOS) using real signals and real noise, rather than just Gaussian noise, is presented. Noisy real signals are processed using various HOS techniques. We propose to look at the diagonal slices of the bispectrum and the trispectrum as possible substitutes for the power spectrum. The result of applying these slices to weak, real signals is surprisingly good. The dramatic improvements are presented for visual inspection. The performance of the various techniques are then compared quantitatively for different signal-to-noise ratios. The diagonal slices prove to be fast and robust techniques for weak signal detection     

A phase reconstruction algorithm from bispectrum [seismicreflection data]

A computationally efficient procedure for the reconstruction of the impulse response of a (minimum- or nonminimum-phase) linear time-invariant system from its bispectrum is presented. This method is based on computing cepstrum of the impulse response sequence from the ω₁=ω₂ slice of the bispectrum. The algorithm can be implemented by using only the one-dimensional fast Fourier transform algorithm     

Signal reconstruction from the phase of the bispectrum

The authors present a simple procedure, the bispectrum signal reconstruction (BSR) algorithm, to recover the Fourier phase of a signal from the phase of its bispectrum. By simple analogy, a procedure that recovers the Fourier magnitude of a signal from the magnitude of its bispectrum is also presented. In addition, the authors propose an iterative scheme, the bicepstrum iterative reconstruction algorithm (BIRA), for the reconstruction of a finite impulse response (FIR) sequence from only the phase of its bispectrum, and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm. Both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the Fourier phase of the signal, whereas their sums contain the Fourier-magnitude information     

A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. We propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.     

基于双谱理论的雷达辐射源指纹特征提取

针对雷达辐射源指纹特征提取困难的问题,提出了基于双谱切片法和双谱围线积分法,提取辐射源指纹特征的方法。介绍了二相编码信号的无意调制,仿真了理想情况和含有相位噪声的二相编码信号的时域波形。阐述了含相位噪声雷达信号的双谱估计,仿真了含相位噪声的二相编码信号的双谱图及等高图。最后利用双谱切片法和双谱围线积分法,提取了辐射源的指纹特征,通过计算机仿真实验验证了该方法的可实施性。     

Texture decomposition by harmonics extraction from higher order statistics

In this paper, a method of harmonics extraction from Higher Order Statistics (HOS) is developed for texture decomposition. We show that the diagonal slice of the fourth-order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies. We propose to use this fourth-order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted. Hence, a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a Wold-like decomposition procedure. The simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods.     

Bispectral analysis and reconstruction in the frequency domain of mono- and bidimensional deterministic sampled signals

Deterministic sampled signals bispectra are periodic and hold more information than analog signal bispectra. After showing this difference, the communication presents two algorithms for reconstructing a sampled signal Fourier transform from its bispectrum: the first is a least squares reconstruction method deducing the Fourier transform logarithm from the bispectrum logarithm through a simple average; the second is an algorithm for reconstructing the Fourier transform from a restricted number of values on the bispectrum diagonal slice by a simple resolution of linear equations. The resistance of both algorithms to the measurement noise is given.     

一种新的雷达辐射源信号识别方法研究

随着雷达技术的发展,雷达体制的多样性和雷达信号的复杂性对雷达辐射源信号识别技术提出了严峻的挑战。循环双谱抗噪性能强,且包含了丰富的信息,能用于识别雷达辐射源信号。但是其数据量庞大,而循环双谱对角切片法丢失了大部分信息。证明了循环双谱的对称性和周期性,提出了局部轴向积分循环双谱。该方法首先计算信号的循环双谱,然后在两个谱频率构成的平面上沿平行于谱频率轴的直线积分,最后用Fisher判决率（FDR）选择鉴别能力较强的轴向积分循环双谱。这样不但能有效地减小数据量,而且保留了大部分有用的循环双谱信息。仿真条件下,对比分析了局部轴向积分循环双谱与循环双谱对角切片的识别效果,结果表明新方法的识别率远远优于循环双谱对角切片法。      

A 3D reconstruction of vascular structures from two X-ray angiograms using an adapted simulated annealing algorithm

A three-dimensional (3D) reconstruction of the vessel lumen from two angiographic views, based on the reconstruction of a series of cross-sections, is proposed. Assuming uniform mixing of contrast medium and background subtraction, the cross-section of each vessel is reconstructed through a binary representation. A priori information about both the slice to be reconstructed and the relationships between adjacent slices are incorporated to lessen ambiguities on the reconstruction. Taking into account the knowledge of normal vessel geometry, an initial solution of each slice is created using an elliptic model-based method. This initial solution is then deformed to be made consistent with projection data while being constrained into a connected realistic shape. For that purpose, properties on the expected optimal solution are described through a Markov random field. To find an optimal solution, a specific optimization algorithm based on simulated annealing is used. The method performs well both on single vessels and on branching vessels possessing an additional inherent ambiguity when viewed at oblique angles. Results on 2D slice independent reconstruction and 3D reconstruction of a stack of spatially continuous 2D slices are presented for single vessels and bifurcations.     

基于双谱的谐波信号相位重构

本文提出了一种基于双谱分析的谐波信号相位精确重构方法.该方法通过在被测信号中加入一相位为零的半基频信号,并对该合成信号进行双谱分析,实现了被测信号的相位精确求解,解决了已有基于双谱的信号相位估计方法中所存在的相对相移问题.仿真结果验证了该方法的有效性.     

Performance Study of Adaptive Filtering in Bispectrum Signal Reconstruction

The problem of reconstructing a signal waveform when the observed realizations are corrupted by intensive noise and random shifts is considered in this paper. Several ways of performing bispectrum filtering are proposed and investigated. First, it is shown that the signal reconstruction is more efficient if one applies smoothing to the recovered real and imaginary parts of the Fourier spectrum separately instead of filtering the magnitude and phase spectra recovered from a bispectrum estimate. Second, several nonadaptive filters are studied, and it is demonstrated that the proper choice of the filter type and its parameters is critical. Some adaptive filtering techniques based on the Z-parameter and on local polynomial approximation (LPA)-intersection of confidence intervals (ICI) are discussed. The performances of nonadaptive and adaptive filtering techniques in the bispectrum-based signal reconstruction are studied using the mean-squared error as the criterion. It is shown that the use of LPA-ICI and other adaptive filters provides improvement of signal reconstruction in comparison to the conventional bispectrum method and the combined bispectrum filtering methods proposed earlier for nonadaptive filters. The benefits achieved are mainly observed for low (smaller than unity) signal-to-noise ratios.     

应用复双谱对角切片的雷达多目标特征提取

提出了应用Chirp-z变换把依赖于傅里叶变换的双谱对角切片扩展为可在z平面上选择任意变换路径和任意频率分辨率的复双谱对角切片,并作为多目标模式的分类特征,能获取双谱以外的可分性特征。为压缩特征维数,选择可分性最好的特征,提出了实用的距离准则,在两类模式情况下,该准则等于Fisher准则,用于多类模式比Fisher准则更易于选择特征。最后应用上述方法,给出了雷达多目标特征提取的实验结果。     

Capturing asymmetry in distortion of an RF system using a multislice behavioral model

Baseband effects result in asymmetrical distortion of RF communication signals through the interaction of baseband-related distortion with in-channel distortion. Here, a behavioral model architecture that captures these asymmetries and can be implemented in a variety of circuit and system simulators is presented. The architecture has two or more slices with each slice corresponding to different frequency bands or multiple parallel nonlinear processes. Each slice could comprise any conventional narrow-band functional model. Here, the behavioral model is extracted using AM-AM and AM-PM measurements for the first slice and phase and amplitude measurement of intermodulation components for the second slice.     

Image restoration using the W-slice method

We propose the use of higher order statistics (HOS)-based methods to address the problem of image restoration. The restoration strategy is based on the fact that the phase information of the original image and its HOS are not distorted by some types of blurring. The difficulties associated with the combination of 2-D signals and their HOS are reduced by means of the Radon transform. Two methods that apply the weight-slice algorithm over the projections are developed. Simulation results illustrate the performance of the proposed methods.     

Detection of quadratic phase coupling from human EEG signals using higher order statistics and spectra

Interactions among neural signals in different frequency components have become a focus of strong interest in biomedical signal processing. The bispectrum is a method to detect the presence of quadratic phase coupling (QPC) between different frequency bands in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index (BCI), which is essentially a normalized bispectrum. The main disadvantage of the BCI is that the determination of significant QPC becomes compromised with noise. To mitigate this problem, a statistical approach that combines the bispectrum with an improved surrogate data method to determine the statistical significance of the phase coupling is introduced. The method was first tested on two simulation examples. It was then applied to the human EEG signal that has been recorded from the scalp using international 10–20 electrodes system. The frequency domain method, based on normalized spectrum and bispectrum, describes frequency interactions associated with nonlinearities occurring in the observed EEG.     

2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data

True three-dimensional (3-D) volume reconstruction from fully 3-D data in positron emission tomography (PET) has only a limited clinical use because of its large computational burden. Fourier rebinning (FORE) of the fully 3-D data into a set of 2-D sinogram data decomposes the 3-D reconstruction process into multiple 2-D reconstructions of decoupled 2-D image slices, thus substantially decreasing the computational burden even in the case when the 2-D reconstructions are performed by an iterative reconstruction algorithm. On the other hand, the approximations involved in the rebinning combined with the decoupling of the image slices cause a certain reduction of image quality, especially when the signal-to-noise ratio of the data is low. We propose a 2.5-D Simultaneous Multislice Reconstruction approach, based on the series expansion principle, where the volume is represented by the superposition of 3-D spherically symmetric bell-shaped basis functions. It takes advantage of the time reduction due to the use of the FORE (2-D) data, instead of the original fully 3-D data, but at the same time uses a 3-D iterative reconstruction approach with 3-D basis functions. The same general approach can be applied to any reconstruction algorithm belonging to the class of series expansion methods (iterative or noniterative) using 3-D basis functions that span multiple slices, and can be used for any multislice sinogram or list mode data whether obtained by a special rebinning scheme or acquired directly by a PET scanner in the 2-D mode using septa. Our studies confirm that the proposed 2.5-D approach provides a considerable improvement in reconstruction quality, as compared to the standard 2-D reconstruction approach, while the reconstruction time is of the same order as that of the 2-D approach and is clinically practical even on a general-purpose computer.     

复AR双谱及在常规雷达目标分类中的应用

根据飞机喷气发动机调制(JEM)特征产生机理和参数模型及常规雷达回波特点,本文采用复AR双谱技术分析了常规雷达回波中的JEM特征,揭示了回波中JEM频率和径向Doppler频率之间的耦合关系,并从双谱切片中提取了相对不变的JEM周期特征。提出了基于JEM周期特征的目标分类方法。实测数据分类实验表明:JEM周期特征用于常规雷达飞机目标分类是有效的。     

QoS路由选择:问题与解决方法综述

保证服务质量的QoS路由(Quality of Service Routing)是网络中解决QoS问题的一项关键技术.QoS路由的主要目标是为接入的业务选择满足服务质量要求的传输路径,同时保证整个网络资源的有效利用.度量参数选择问题、寻路问题和路由信息不准确问题是QoS路由中的几个主要研究内容.本文围绕这三个方面,介绍了QoS路由中的主要问题及相关的解决办法,并探讨了今后QoS路由可能的研究方向.