Detection of the chaotic process distorted by the white noise using BDS statistics

A nonparametric criterion for the detection of a chaotic process observed against the background of white noise has been proposed with due regard for the dependence of the process values. BDS statistic is used for the numerical account of the degree of dependence of values of the process observed. It was shown that this criterion refined the conventional estimate of the chaotic process stealthiness that was obtained using the energy criterion for detecting deterministic signals of the unknown “waveform” and random processes. Characteristics of a nonparametric detector of chaotic processes with a different degree of the dependence of its values were obtained on the basis of computer simulation under condition of the exposure to additive white Gaussian noises of different intensity.     

Harmonic retrieval in colored non-Gaussian noise using cumulants

This paper addresses the harmonic retrieval problem in colored linear non-Gaussian noise of unknown covariance and unknown distribution. The assumptions made in the reported studies that the non-Gaussian noise is asymmetrically distributed and no quadratic phase coupling occurs are released. Using the elaborately defined fourth-order cumulants of the complex noisy observations, which are obtained by Hilbert transform, we can estimate either the correlation or the AR polynomial of the non-Gaussian noise via cumulant projections or ARMA modeling; then, the prewhitening or prefiltering techniques can be employed to retrieve harmonics, respectively. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms     

Direction finding in the presence of colored noise by candidateidentification

A method is developed for identifying correct angles of arrivals from a set of candidate angles that contains spurious angles and the true ones, under the assumption that the colored noise is an autoregressive process and that a uniform linear array of sensors is used. The procedure is based on a relation derived for the higher-order reflection coefficients corresponding to the autocorrelation sequence of the signal plus noise. It is shown that the higher-order reflection coefficients of a set of plane waves impinging on a uniform linear array of sensors, in the presence of an unknown spatially autoregressive colored noise process, are equal to an order independent linear combination of the values of the Fourier transform of the corresponding optimal linear least squares normalized prediction error filter at the electric phase angles of the plane waves. The magnitudes of the coefficients are then used to decide whether a given candidate direction of arrival corresponds to an actual plane wave or not. The estimation of candidate angles is also briefly discussed     

Efficient generation of colored noise

A new technique is presented for efficiently generating colored noise. Instead of discarding initial samples to account for the transient, the approach proposed here is to set the initial conditions of the filter so that the output process will be stationary. It is shown that the Levinson-Durbin algorithm provides an efficient means for determining these initial conditions.     

The quantization noise spectrum of a sinusoid in colored noise

The power density spectrum (PDS) of analog-to-digital (A/D) quantization noise is obtained for an input signal consisting of sinusoid and colored noise. While this type of quantization noise is often assumed to be uncorrelated or white, it may not be when the input signal occupies a relatively small number of quantization levels. Equations describing the PDS are derived and presented for combinations of deterministic and random A/D converter inputs     

抑制电子电路中空间干扰噪音的措施

在进行电子产品开发过程中,必然会遇到各种各样的噪音。为了揭示空间噪音的根源、传输途径及抑制方法.在实验中,反复采用系统接地和电磁屏蔽有效结合的手段,对电路信号中的空间噪音波形进行观察、比较与分析。实践中,使用这些措施去抑制电子产品的空间噪音,都达到了事半功倍的效果。     

The use of BDS statistics for estimating the parameters of chaotic mappings and regular signals in the presence of noise

A new method has been proposed in this paper for estimating the parameters of chaotic and regular signals by their observation against the background of white noise under conditions of the a priori uncertainty about the distribution of its values. The method is based on using the nonparametric BDS statistic revealing the sensitivity toward topological properties of the attractors of chaotic, regular and random processes that are characterized by the correlation dimension. The results of numerical simulation of the method proposed for the estimation of parameters of one-dimensional and two-dimensional chaotic mappings and also the harmonic oscillation frequency for the noise with uniform and Gaussian distribution at different levels of its intensity have been presented. This study also includes the analysis of accuracy of estimating the harmonic oscillation frequency by the proposed method and its comparison with potentially attainable values.     

DOA estimation in unknown colored noise using covariance differencing and sparse signal recovery

A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.     

Harmonics in multiplicative and additive noise: parameterestimation using cyclic statistics

The problem of concern here is parameter estimation of harmonics in the presence of multiplicative and additive noise. Cyclic statistics are employed to estimate the frequencies and phases, after which the time series is demodulated and cumulants of the noise processes are estimated. The latter are then supplied to linear or nonlinear cumulant-based algorithms to identify ARMA model parameters for the noises. Cyclic statistics and higher order spectra-based approaches are shown to yield the same frequency estimates. Simulation examples illustrate the algorithms     

联合投影逼近子空间跟踪的语音增强算法

本文提出一种联合投影逼近子空间跟踪(UPAST)的语音增强算法。本算法以投影逼近子空间跟踪算法为基础, 在无需对噪声进行任何假定(白噪声或是有色噪声)或近似且不需要任何语音活动检测的前提下,以递推更新的方式得到 语音信号和噪声信号协方差矩阵同时对角化的特征向量和特征值,因而运算复杂度低,实现了有色噪声背景下语音信号的 最优估计。主观和客观测试都表明本算法要优于其它子空间增强算法。     

Shaping filter representation of nonstationary colored noise

The problem of determining a shaping filter for nonstationary colored noise is considered. The shaping filter transforms white noise into a possibly nonstationary random process (having no white noise component) with a specified covariance function. A set of conditions to be satisfied by the covariance function leads to the determination of a shaping filter. The shaping filter coefficients are simply related to the solution of a matrix Riccati equation. In order to formulate the Riccati equation, basic results concerning the mean-square differentiability of a random process are developed. If the Riccati equation can not be defined, an autonomous (zero-input) shaping filter may be easily determined.     

Accurate identification of periodic oscillations buried in white or colored noise using fast orthogonal search

We use a previously introduced fast orthogonal search algorithm to detect sinusoidal frequency components buried in either white or colored noise. We show that the method outperforms the correlogram, modified covariance autoregressive (MODCOVAR) and multiple-signal classification (MUSIC) methods. Fast orthogonal search method achieves accurate detection of sinusoids even with signal-to-noise ratios as low as -10 dB, and is superior at detecting sinusoids buried in 1/f noise. Since the utilized method accurately detects sinusoids even under colored noise, it can be used to extract a 1/f noise process observed in physiological signals such as heart rate and renal blood pressure and flow data.     

On the detection of a signal in colored noise

A modeling approach is used in the detection of a random signal in colored noise. The received sequence is modeled as a regressive/autoregressive time series, and the presence or absence of the desired signal is determined through a hypothesis testing procedure. The test is based on the construction of anF-statistic using likelihood functions. The statistic can be easily incorporated into the computation of the probability of a false alarm, such as required in the processing of radar signals. Results based on simulated data and actual radar data are presented.This research was supported by NSERC Grant No. A3635.     

Bayesian detection and estimation of cisoids in colored noise

The problem of estimating the number of cisoids in colored noise is addressed. It is assumed that the noise can be modeled by an autoregression whose order has also to be estimated. A new criterion is proposed for estimating the number of cisoids and the autoregressive model order, as well as a new algorithm for estimating the cisoidal frequencies. In the derivation, a Bayesian methodology and subspace decomposition are employed. The proposed criterion significantly outperforms the popular MDL and AIC as applied in a paper by Nagesha and Kay. In addition, an algorithm that reduces the computational complexity of the solution is developed, computer simulations that demonstrate the performance of the criterion are included     

非高斯色噪声条件下的最小二乘单音频率估计

提出一种非高斯色噪声条件下的最小二乘单音频率估计算法,该算法首先将待估计单音频率搬移至零频附近,然后通过抽取滤波把噪声转换为高斯白噪声,最后引入相位差分最小二乘频率估计构成整个算法.该方法摆脱了FFT类算法频率分辨率的束缚,可以为自动调制识别等应用提供高精度的符号速率估计.     

Maximum likelihood estimation for array processing in colored noise

Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented     

高斯色噪声下的相干信号 DOA 高分辨率估计*

针对高斯有色噪声下的DOA估计问题,提出一种基于高阶累积量稀疏表示的DOA估计方法。该方法利用四阶累积量矩阵中的第一列生成最小冗余向量,利用扩展阵列的最小冗余导向矢量构造过完备字典。然后利用L1范数作为稀疏约束条件,建立最小冗余向量的稀疏模型进行DOA估计。该方法将求解四阶累积量的次数从M4次降为M2-M+1次。同时又能充分利用四阶累积量的优点,对高斯有色噪声具有良好的抑制能力,并使阵列孔径得到了扩展,估计信号个数能大于阵元数目。仿真实验和理论分析验证了该方法比MUSIC-like和MUSIC算法具有更好的性能,不需要任何处理可以直接应用到相干信号。     

On estimating spectral moments in the presence of colored noise

Let{q^(1) (t)}, the signal, be a complex Gaussian process corrupted by additive Gaussian noise{q^(2) (t) }. Observations onp(t)q(t)andp(t) q^(2) (t)are assumed to be available wherep(t)is a smooth weighting function andq = q^(1) + q^(2). Using the Fourier transform of the samples ofp(t)q(t)andp(t) q^(2) (t), estimators are derived for estimating the mean frequency and spectral width of the unknown power spectrum of the unweighted signal process. The means and variances of these statistics are computed in general, and explicitly for nontrivial practical examples. Asymptotic formulas for the moment estimators as a function of the number of realizations, frequency resolution, signal-to-noise ratio and spectral width, and consistency of the estimators are some of the results that are discussed in detail.     

Filtering of colored noise for speech enhancement and coding

Scalar and vector Kalman filters are implemented for filtering speech contaminated by additive white noise or colored noise, and an iterative signal and parameter estimator which can be used for both noise types is presented. Particular emphasis is placed on the removal of colored noise, such as helicopter noise, by using state-of-the-art colored-noise-assumption Kalman filters. The results indicate that the colored noise Kalman filters provide a significant gain in signal-to-noise ratio (SNR), a visible improvement in the sound spectrogram, and an audible improvement in output speech quality, none of which are available with white-noise-assumption Kalman and Wiener filters. When the filter is used as a prefilter for linear predictive coding, the coded output speech quality and intelligibility are enhanced in comparison to direct coding of the noisy speech