Classification of nonstationary narrowband signals using segmented chirp features and hidden Gauss-Markov models

A method is provided for classifying finite-duration signals with narrow instantaneous bandwidth and dynamic instantaneous frequency (IF). In this method, events are partitioned into nonoverlapping segments, and each segment is modeled as a linear chirp, forming a piecewise-linear IF model. The start frequency, chirp rate, signal energy, and noise energy are estimated in each segment. The resulting sequences of frequency and rate features for each event are classified by evaluating their likelihood under the probability density function (PDF) corresponding to each narrowband class hypothesis. The class-conditional PDFs are approximated using continuous-state hidden Gauss-Markov models (HGMMs), whose parameters are estimated from labeled training data. Previous HGMM algorithms are extended by dynamically weighting the output covariance matrix by the ratio of the estimated signal and noise energies from each segment. This covariance weighting discounts spurious features from segments with low signal-to-noise ratio (SNR), making the algorithm more robust in the presence of dynamic noise levels and fading signals. The classification algorithm is applied in a simulated three-class cross-validation experiment, for which the algorithm exhibits percent correct classification greater than 97% as low as -7 dB SNR.     

System identification using nonstationary signals

The conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output. It is equivalent to identifying the frequency response of the system by calculating the empirical cross-spectrum between the system's input and output, divided by the empirical auto-spectrum of the input process. However, if the additive noise at the system's output is correlated with the input process, e.g., in case of environmental noise that affects both system's input and output, the method may suffer from a severe bias effect. We present a modification of the cross-spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise. The proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation, when the desired signal is nonstationary in nature, e.g., speech or image     

Algorithm for the Wigner distribution of noisy signals realisation

A simple robust algorithm which efficiently represents signals with a very high amount of noise is presented, according to the expressions for the mean, variance and the optimal window width of the Wigner distribution estimator. Its application in time-varying filtering is illustrated     

Blind channel equalization using chirp modulating signals

This paper addresses the problem of blind channel equalization in the context of digital communications. Recent results have shown that certain operations applied to the source signal at the transmitter help in the blind identification and equalization of the channel at the receiver. In this paper, the baseband data signal is multiplied with a chirp sequence. Exploiting certain structural properties arising from this operation, a batch-type algorithm is obtained for calculating the equalizer's coefficients. Conditions on the chirp sequence parameters are obtained that guarantee an equalization solution. A low-complexity adaptive algorithm is also proposed. Finally, extensive simulations, and comparisons with other well-known blind techniques, illustrate the excellent performance of this algorithm.     

基于Wigner分布的脑电信号处理

临床实践表明,脑电信号中包含有大量的生理与疾病信息。对脑电信号进行行之有效的处理,不仅可以为医生提供临床诊断信息,而且可以为某些脑疾病的治疗提供有效的治疗手段。目前,随着信号处理技术的发展,在脑电信号处理中已应用了多种信号分析方法来提取脑电信号中所包含的信息,但大多数还是停留在理论研究阶段。本文在研制虚拟式脑电图仪的过程中,考虑到Wigner分布在各种时频分布中具有最简单的形式和良好的性质,从临床应用及医学研究相结合的角度出发,应用Wigner分布对脑电信号进行时频分析以提取脑电信号中的特征信息。对实测脑电数据的分析表明,应用此方法可获得较好的分析效果。     

The Wigner distribution of a linear signal space

A time-frequency representation of linear signal spaces, called its Wigner distribution (WD), is introduced. Similar to the WD of a signal, the WD of a linear signal space describes the space's energy distribution over the time-frequency plane. It is shown that the WD of a signal space can be defined both in a deterministic and in a stochastic framework, and it can be expressed in a simple way in terms of the space's projection operator and the bases. It is shown to satisfy many interesting properties which are often analogous to corresponding properties of the WD of a signal. The results obtained for some specific signal spaces are found to be intuitively satisfactory. The cross-WD of two signal spaces, a discrete-time WD version, and the extension of the WD definition to arbitrary quadratic signal representation are also discussed     

The Wigner distribution of noisy signals with adaptivetime-frequency varying window

Time-frequency representations using the Wigner distribution (WD) may be significantly obscured by the noise in the observations. The analysis performed for the WD of discrete-time noisy signals shows that this time-frequency representation can be optimized by the appropriate choice of the window length. However, the practical value of this analysis is not significant because the optimization requires knowledge of the bias, which depends on the unknown derivatives of the WD. A simple adaptive algorithm for the efficient time-frequency representation of noisy signals is developed in this paper. The algorithm uses only the noisy estimate of the WD and the analytical formula for the variance of this estimate. The quality of this adaptive algorithm is close to the one that could be achieved by the algorithm with the optimal window length, provided that the WD derivatives were known in advance. The proposed algorithm is based on the idea that has been developed in our previous work for the instantaneous frequency (IF) estimation. Here, a direct addressing to the WD itself, rather than to the instantaneous frequency, resulted in a time and frequency varying window length and showed that the assumption of small noise and bias is no longer necessary. A simplified version of the algorithm, using only two different window lengths, is presented. It is shown that the procedure developed for the adaptive window length selection can be generalized for application on multicomponent signals with any distribution from the Cohen (1989, 1990, 1992) class. Simulations show that the developed algorithms are efficient, even for a very low value of the signal-to-noise ratio     

Parametric estimation of 2D cubic phase signals using high-order Wigner distribution with genetic algorithm

Multidimensional Systems and Signal Processing - A two-dimensional (2D) high-order Wigner distribution (HO-WD) is proposed for parameter estimation of 2D polynomial phase signals (PPSs). The...     

Classification of chirp signals using hierarchical Bayesianlearning and MCMC methods

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm     

Filtering of nonstationary signals using predictor median hybrid structures

An approach to filtering of nonstationary signals that contain abrupt changes from one signal state to another is presented. Proposed nonlinear filters, the Predictor Median Hybrid (PMH) filters, contain substructures to estimate the current signal value using forward and backward prediction. The output of the overall filter is the median of the predicted values and the actual signal value. This kind of nonlinear filter structure is shown to have some interesting properties: (1) Due to the median operation, the filters do not disturb rapid changes from one stationary signal to another and yet they attenuate noise. (2) The predictive substructures can be chosen according to the application, thus greatly extending the class of signals where median type filters can be applied. (3) Due to the predictive nature of the substructures they adapt to the signal, thus simplifying the design of the filters. Two types of predictive substructures have been used: linear predictive substructures and curve fitting based predictors. The PMH filters with linear predictive substructures are shown to be especially useful for the restoration of deterministic and stochastic signals that contain impulse-like distortions. The curve fitting based substructures are shown to be useful for attenuation of Gaussian noise.     

Estimation of instantaneous frequency using the discrete Wigner distribution

Analytical expressions for the performance of the discrete Wigner distribution (DWD) in estimating the instantaneous frequency of linear frequency modulated signals in additive white noise are derived and verified using simulation. It is shown that the DWD peak provides an optimal estimate at high input signal-to-noise ratios. The applicability of these results to the general case of nonlinear FM signals is discussed.<>     

一种基于chirp信号的空间域鲁棒性水印算法

选取两个chirp信号作为水印信息,嵌入到图像空间域中与该信号有相同数字特征的像素点处,使用两个嵌入位置矩阵作为算法密钥的同时,还根据chirp信号在分数傅立叶变换域呈现冲激的特征来检测水印信号。仿真实验结果表明,该数字水印算法具有良好的不可见性和安全性,算法不仅能抵抗很强的JPEG压缩、加噪、滤波等常用的信号处理操作,对旋转、平移、剪切等几何攻击也有很强的鲁棒性。     

System identification using chirp signals and time-variant filtersin the joint time-frequency domain

We propose a novel method to identify an unknown linear time invariant (LTI) system in low signal-to-noise ratio (SNR) environment. The method is based on transmitting chirp signals for the transmitter and using linear time-variant filters in the joint time-frequency (TF) domain for the receiver to reduce noise before identification. Due to the TF localization property of chirp signals, a large amount of additive white noise can be reduced, and therefore, the SNR before identification can be significantly increased. This, however, cannot be achieved in the conventional methods, where pseudo-random signals are used, and therefore, noise reduction techniques do not apply. Our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low SNR environment. This paper provides a good application of time-frequency analysis and synthesis     

Analysis of 3-D integral imaging displays using the Wigner distribution

Integral imaging is a promising technology for 3-D TV and 3-D display. In this paper, a theoretical analysis of 3-D integral imaging systems is performed in the frame of the Wigner distribution formalism. It is shown that the entire intensity distribution in the pick-up image plane of these systems can be obtained from a single 2-D Wigner distribution function of a single lenslet pupil. This result reveals the Wigner distribution function as a powerful tool for analysis of 3-D integral imaging systems with different pupil functions. As an example, the extension of the depth of field of an integral imaging system with lenslets having amplitude modulation (central obscuration) is proposed.     

Iterative parameter estimation of multiple chirp signals

The authors propose an algorithm for estimating the parameters of multiple superimposed chirp signals in additive white noise. The algorithm is based on a novel iterative approach that significantly reduces the error propagation effect inherent in many existing techniques. Moreover, it allows the estimation over a wider range of phase parameter values while still maintaining a better estimation accuracy     

Results on AR-modelling of nonstationary signals

Modelling of nonstationary signals can be performed using time-varying AR-models. The time-dependent AR-coefficients are assumed to be well represented by a linear combination of a small number of known time functions. This paper intends to compare two methods for the identification of such models. The first one is a blockwise method in which the parameters are estimated using the Morf-Dickinson-Kailath-Vieira algorithm for the resolution of covariance equations. In the second method, the identification is performed by a recursive least-squares algorithm. Finally, an extension of the second method for the detection of abrupt changes in AR-processes is presented.     

Nonlinear adaptive prediction of nonstationary signals

We describe a computationally efficient scheme for the nonlinear adaptive prediction of nonstationary signals whose generation is governed by a nonlinear dynamical mechanism. The complete predictor consists of two subsections. One performs a nonlinear mapping from the input space to an intermediate space with the aim of linearizing the input signal, and the other performs a linear mapping from the new space to the output space. The nonlinear subsection consists of a pipelined recurrent neural network (PRNN), and the linear section consists of a conventional tapped-delay-line (TDL) filter. The nonlinear adaptive predictor described is of general application. The dynamic behavior of the predictor is demonstrated for the case of a speech signal; for this application, it is shown that the nonlinear adaptive predictor outperforms the traditional linear adaptive scheme in a significant way     

Tracking nonstationary probabilities in adaptive binary arithmeticcoding

Adaptive arithmetic coders sometimes exhibit nonstationary symbol probabilities when coding digital halftone images with neighborhood-template models. If these nonstationary probabilities vary nonrandomly, the variations can be tracked robustly when each context derived from the coding model is expanded by conditioning on previously coded values for that model context.     

基于正负斜率线性调频脉冲信号的一种新的测速方法

提出了一种基于正负斜率线性调频脉冲信号进行目标测速的方法,通过分析两次MTD后的距离维信息和多普勒维信息,分别对速度进行了初步估计和精确测量.综合两次MTD结果得到了目标的实际速度,并推导出了脉冲占空比和速度测量误差的关系式.仿真表明了此方法的正确性,且具有一定的应用价值.