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.     

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.     

Asymptotic Bias and Variance of Conventional Bispectrum Estimates for 2-D Signals

In this paper, we derive the asymptotic bias and variance of conventional bispectrum estimates of 2-D signals. Two methods have been selected for the estimation: the first one – the indirect method – is the Fourier Transform of the weighted third order moment, while the second one – the direct method – is the expectation of the Fourier component product. Most of the developments are known for 1-D signals and the first contribution of this paper is the rigorous extension of the results to 2-D signals. The calculation of the bias of the direct method is a totally original contribution. Nevertheless, we did all calculations (bias and variance) for both method in order to be able to compare the results. The second contribution of this paper consists of the comparison of the theoretical bispectrum estimate bias and variance with the measured bias and variance for two 2-D signals. The first studied signal is the output of a non-minimal phase linear system driven by a non-symmetric noise. The second signal is the output of a non-linear system with Gaussian input data. In order to assess the results, we performed the comparison for both methods with different sets of parameters. We show that the maximum bias coefficient is the one of the 1-D case multiplied by the dimensionality of the signal for both methods. We also show that the estimate variance coefficient is the 1-D case coefficient with a power equal to the signal dimensionality.Received October 21, 2002; Revised December 2003; Accepted March 25, 2004; First Online Version published in December 2004     

Linear bispectrum of signals and identification of nonminimum phaseFIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification     

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     

基于改进ResNet的射频指纹识别方法

在无线网络安全和可能存在的射频设备管理应用范围内,针对多个发射同种射频信号的高度相似射频设备的分类识别问题,提出了一种信号双谱与改进的残差神经网络(Residual Neural Network,ResNet)的射频指纹识别方法.首先,将采集到的不同设备的信号做双谱变换得到双谱等高图并打上设备标签,再使用搭建好的改进残...     

Cross-term elimination in Wigner distribution based on 2D signal processing techniques

An efficient method based on 2D signal processing techniques and fractional Fourier transform is presented to suppress interference terms of Wigner distribution (WD). The proposed technique computes Gabor transform (GT) of a multi-component signal to obtain a blurred time-frequency (t-f) image. Signal components in GT image are segmented using connected component segmentation and are filtered out using precise application of fractional Fourier transform. A crisp t-f representation is then obtained by computing the sum of products of WD and GT of the isolated signal components. The efficacy of the proposed technique is demonstrated using examples of synthetic signals and real-life bat signals. Proposed scheme gives satisfactory performance even when cross-terms of WD overlap auto-terms and computational cost analysis shows that it is more efficient than recent interference suppression techniques of comparable performance. Moreover, the proposed technique does not require any prior info regarding the nature of signal.     

Nonparametric bispectrum-based time-delay estimators for multiplesensor data

When estimating time-delays of signals from sensor outputs, the bispectrum has advantages when the signal has a skewed distribution. The authors provide nonparametric estimation approaches which exploit the two-dimensional nature of the bispectrum. When dealing with observations from more than a pair of sensors, the new algorithms have computational advantages and, in some cases, show improved performance compared to the conventional nonparametric, bispectrum-based time-delay estimation approach     

基于分数低阶统计量的双谱及其估计方法

稳定分布可更好地描述实际中所遇到的具有显著脉冲特性的随机噪声.为了更好地抑制信号背景中的非高斯噪声,本文提出了基于分数低阶的双谱定义,并给出在分数低阶有色噪声背景下双谱非参数和参数模型的估计方法.仿真结果表明,同传统的双谱估计相比较,非参数法分数低阶双谱估计能有效的识别信号,保留了信号的幅度和相位信息,但存在较大的估计方差.基于AR模型的分数低阶双谱估计具有最大的谱平坦度,能够有效地抑制噪声,具有良好的韧性.     

AR model order selection based on bispectral cross correlation

A novel method is presented for optimal model order selection for autoregressive (AR) bispectrum estimation. The method depends solely on the data and requires no a priori information about the process. The method selects the model order that maximizes the cross correlation between the direct (fast Fourier transform-based) bispectrum estimate and the autoregressive bispectrum estimate. Simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise     

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     

Development and application of a statistically based feature extraction algorithm for monitoring tool wear in Circuit Board Assembly

Vibroacoustic signals of rotating machinery are composed of sums of modulated periodicities, broadband random components, and occasionally a set of transient responses. These signals are not ergodic as the modulated periodicities are partially coherent. Progressive wear of the rotating machine causes the nonlinear structure of the received signal to intensify, and nonlinearity results in transfer of energy between harmonics of the signal's periodic components. Statistics developed from bispectrum and second-order cumulant spectrum estimates of the measured signal are combined with power spectrum amplitudes as feature inputs for standard multivariate classifiers. The higher-order statistics measure, respectively, the extent of nonlinearity and intermodulation of the received signal. Classification results of simulated and actual incipient wear data collected from a controlled experiment drilling circuit boards illustrate the potential of this novel statistical signal processing approach.     

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。      

Noise reduction in rhythmic and multitrial biosignals with applications to event-related potentials

A new noise reduction algorithm is presented for signals displaying repeated patterns or multiple trials. Each pattern is stored in a matrix, forming a set of events, which is termed multievent signal. Each event is considered as an affine transform of a basic template signal that allows for time scaling and shifting. Wavelet transforms, decimated and undecimated, are applied to each event. Noise reduction on the set of coefficients of the transformed events is applied using either wavelet de- noising or principal component analysis (PCA) noise reduction methodologies. The method does not require any manual selection of coefficients. Nonstationary multievent synthetic signals are employed to demonstrate the performance of the method using normalized mean square error against classical wavelet and PCA based algorithms. The new method shows a significant improvement in low SNRs (typically <0 dB). On the experimental side, evoked potentials in a visual oddball paradigm are used. The reduced-noise visual oddball event-related potentials reveal gradual changes in morphology from trial to trial (especially for N1-P2 and N2-P3 waves at Fz), which can be hypothetically linked to attention or decision processes. The new noise reduction method is, thus, shown to be particularly suited for recovering single-event features in non- stationary low SNR multievent contexts.     

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.     

Spectral analysis of atmospheric radar signal using higher orderspectral estimation technique

Higher order spectral estimation techniques have been applied to the backscattered signals received from the troposphere and lower stratosphere by the Gadanki mesosphere-stratosphere-troposphere (MST) radar. These techniques allow identification of signals that have non-Gaussian probability distribution. To understand these processes and their effect on estimation of the atmospheric parameters, power spectrum, and bispectrum analyses have been performed on the signals received in both vertical and off-vertical directions. The results show that the backscattered echoes received in the vertical direction are significantly non-Gaussian, while those received in the off-vertical direction are inferred to have predominant Gaussian component. It is demonstrated that the bispectral analysis technique has capability for estimating the vertical wind component with greater accuracy than that derived from the commonly employed fast Fourier transform based power spectral technique     

一种基于Kay瞬时测频的PSK解码方法

在电子侦察中,需要判断截获的雷达信号的调制方式和调制参数。利用Kay瞬时测频结合聚类分析的方法,可检测LFM、FSK和PSK信号。对相位编码信号,利用单脉冲多重相关积累算法从信号中提取相位跳变规律,并在此基础上给出了相位编码序列恢复方法。该处理方法在信噪比较高时,计算速度优于短时傅里叶变换(STFT)等方法。最后,通过计算机仿真显示了该方法具有较好的精度和处理结果。     

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.     

基于短时傅里叶变换测向技术

针对传统测向算法对短时信号测向性能差的问题,提出了一种基于短时傅里叶变换(Short-time Fourier Transform,STFT)的频域处理与信号功率门限的自动判决相结合的测向技术,在除去干扰信号的同时提取目标信号的有效信息,然后利用测向算法进行测向。给出了该算法的具体实现过程,并对算法进行了仿真分析,验证其可行性,同时给出了仿真结果并指出了算法的优点与不足。