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     

基于DDS的任意频谱信号重构与数字正交调制方法

任意频谱信号产生方法是将功率谱转换为矢量频谱,再经傅立叶反变换,对得到的多个时域数据序列进行加窗、搭接得到一个长的时间序列,用该序列去逼近任意频谱信号对应的时域无限长序列,最后经过数字正交调制重构出任意频谱信号。计算机仿真分析表明,本文方法的理论重构精度达80dB以上,通过直接数字频率合成技术（DDS）实现的数字正交调制器的实际输出信噪比达65dB以上。     

Waveform estimation from noisy signals with variable signal delayusing bispectrum averaging

A technique based on bispectrum averaging is described for generally recovering the signal waveform from a set of noisy signals with variable signal delay. The technique does not require explicit time alignment of signals and any initial estimate of signal. The technique, however, does not yield estimates of the signal position. A comparison is made of two algorithms for recovering the Fourier amplitude and the Fourier phase from an averaged bispectrum. These algorithms are the recursive method and the least squares method. The methods are numerically investigated using computer-generated data and a physiological signal and noise. The advantages and disadvantages of these different algorithms are discussed. Some experimental results for the evoked potential studies that demonstrate the technique are given. The results show the effectiveness of the technique: various potential applications of the technique might be expected     

Pattern recognition using invariants defined from higher orderspectra: 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants     

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     

用对数平均双谱识别飞机的原理和方法

文章首先定义了对数双谱并给出了与目标识别有关的三个性质,接着推导了目标对数双谱与高分辨距离像对数双谱之间的关系,由此提出了对数双谱自动目标识别的距离准则和实现方法.外场实测数据的计算机仿真表明,该方法适用于飞机识别,是有效的和可行的.     

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.     

Modeling arbitrary polynomial bispectra in one and two dimensions

The authors propose a novel model, called a system with multiplicity (SWM), which is a refinement of the model proposed by Sakaguchi and Sakai (1989), to represent arbitrary polynomial bispectra. It is shown that an arbitrary polynomial bispectrum of a 1-D signal can always be realized using an SWM with FIR (finite impulse response) components. An algorithm is then developed for the identification of SWM that will match a given polynomial bispectrum. The authors address the problem of simultaneously matching an arbitrary polynomial bispectrum and a rational power spectrum function using an SWM. It is shown that this can always be accomplished by including another LSI component that is driven by a Gaussian input to the system. Experimental results for matching an estimated bispectrum as well as simultaneously matching a polynomial bispectrum and a power spectrum of some 1-D signals are presented. It is shown that in two dimensions an arbitrary polynomial bispectrum cannot always be uniquely modeled using an SWM with 2-D FIR components having different extents     

高阶累积量在红外热像损伤检测信号分析中的应用

针对常规红外检测信号的脉冲相位法没有考虑测量噪音,简单的Fourier变换对数据信息的挖掘不足、利用率不高的问题,提出在处理中引入非高斯特性分析,应用三阶累积量和双谱估计对信号进行分析,提取发生损伤时信号的特性信息,得到分辨完好区域与损伤区域的特征判据。给出信号分析中三阶累积量和双谱的定义,分析其幅值和相位的对角切片谱在提取损伤特征方面的优势,最后对比分析两者在实际检测中的效果。结果表明:利用该方法具有良好的抗高斯和非高斯对称分布型噪音的优点,且运算量小、计算速度快。同时,弥补了传统脉冲相位法中幅值谱不宜使用的缺点。     

Analytical formulae for reconstruction of certain discrete signalsfrom phase level and line crossings

We provide simple and explicit formulae for reconstructing any member of a class of discrete-time signals from the frequencies at which its Fourier phase crosses any specific level of constant phase or a linear-phase line with integer slope, provided that the number of crossings equals the length of the signal support. Unlike previous closed-form solutions, solution of an ill-conditioned system of linear equations is not required. The associated uniqueness results reduce, in special cases, to previous results for reconstruction from Fourier transform real and imaginary part zero crossings     

分数阶傅里叶变换域上带通信号的采样定理

傅里叶变换和采样定理是信号处理领域的两大基本问题,采样定理研究了傅里叶变换域上带限信号的采样和重构理论.分数阶傅里叶变换(FRFT)是傅里叶变换的一种推广,与之相应的采样理论目前还不十分完备,所以有必要从FRFT域上重新研究采样定理.本文首先得到了均匀冲激串采样信号的FRFT,然后在此基础上导出了FRFT域上带通信号和低通信号的采样定理和重构公式.这些结果是经典理论的推广,将丰富分数阶傅里叶变换的理论体系.     

The gridding method for image reconstruction by Fourier transformation

The authors explore a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f;. The method involves a window function w; and proceeds in three steps. First, the convolution g;=w;*f; is computed numerically on a Cartesian grid, using the available samples of f;. Then, g=wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w;*f; is much less error prone than merely interpolating f;. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.     

基于一维选择线谱的脉冲星辐射脉冲信号辨识

为提高脉冲星辐射脉冲信号辨识效果,利用双谱技术提取了脉冲星累积脉冲轮廓的非线性和非高斯特征.提出了一维选择线谱辨识算法,该算法采用特征核与特征域描述统计信号的共性及个性,定义信号特征矢量方差及特征矢量间的距离,抽取双谱图中具有最强类别可分离度的一维线谱特征向量构成特征模板.实验结果表明:一维选择线谱特征向量适于脉冲星信号辨识,且与选择双谱相比,一维选择线谱算法使整个特征向量具有最大类间可分离度,可以获得更好的辨识效果.     

线性正则变换域的带限信号采样理论研究

线性正则变换是傅里叶变换、分数阶傅里叶变换的更广义形式,是一种潜在而重要的信号变换工具,但是与之相应的采样理论目前还不十分完备,所以有必要在线性正则变换域重新研究采样定理.本文从线性正则变换的定义和性质出发,首先得到时域均匀采样信号的线性正则变换;然后在此基础上导出了线性正则变换域带限信号的采样定理和重构公式;最后以chirp信号为例仿真说明了采样定理的应用.文中得出的结论是对经典采样理论的推广,将进一步丰富线性正则变换的理论体系.     

分数阶Fourier域上非均匀采样信号的频谱重构研究

 本文研究了分数阶Fourier变换域上非均匀采样信号的重构问题.首先得到周期非均匀采样信号经非均匀分数阶Fourier变换后的频谱表达式,研究了该分数阶频谱和信号连续分数阶频谱之间的关系,并基于该关系式提出了一种分数阶Fourier域周期非均匀采样信号的频谱重构算法;其次,讨论了分数阶Fourier变换域上更加一般情况下非均匀采样信号重构问题;最后,给出了周期非均匀采样信号频谱重构的仿真结果.     

Mean and variance of estimates of the bispectrum of a harmonicrandom process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework     

单目标一维成像及特征提取方法性能分析

为后续目标识别作准备,针对采集并且存储之后的飞机目标雷达回波信号,完成后端雷达信号处理.首先,基于MATLAB提取波门内采样的回波信号并且实现目标的一维成像.然后,采用传统的傅里叶变换模值、双谱奇异值分解法对目标的一维距离像进行特征提取.为了获得较为稳定的目标特征,针对以上两种方法,主要从特征相似性的测量角度分析单一目标特征提取方法的性能优劣.最后通过实验,从相关系数概率密度分布情况得出双谱奇异值分解特征提取法性能较佳,所得到的目标特征较稳定.     

一种雷达辐射源双谱二次特征提取方法

针对常规参数进行复杂体制雷达辐射源信号分选时存在的问题,对信号双谱图分别进行频率分区和奇异值分解,二次提取其双谱分布熵和奇异谱熵作为雷达辐射源特征参数.该方法利用双谱分析可以完全抑制高斯有色噪声对信号的影响,同时保留信号的幅度和相位信息的特点,并有机地融合了双谱理论、奇异值分解和信息熵理论的各自优点,反映出信号的本质信息.采用模糊C均值聚类算法对不同信噪比条件下6种典型调制类型的雷达辐射源信号进行聚类分选实验.实验结果表明,该方法取得了较好的分选效果,克服了传统图像特征提取算法特征维数过高和聚集性差的缺点,验证了该方法的有效性.     

Iterative algorithm for nonuniform inverse fast Fourier transform(NU-IFFT)

A nonuniform inverse fast Fourier transform (NU-IFFT) for nonuniformly sampled data is realised by combining the conjugate-gradient fast Fourier transform (CG-FFT) method with the newly developed nonuniform fast Fourier transform (NUFFT) algorithms. An example application of the algorithm in computational electromagnetics is presented     

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