A model order selection criterion with applications to cardio-respiratory-renal systems

We introduce a model order selection criterion called signal prediction error (SPE) for the identification of a linear regression model, which can be an adequate representation of a resting physiologic system. SPE is an estimate of the prediction error variance due only to model estimation error and not unobserved noise, which distinguishes it from the widely used final prediction error (FPE). We then present a theoretical analysis of SPE, which predicts that its ability to select correctly the model order is more dependent on the signal-to-noise ratio (SNR) and less dependent on the number of data samples available for analysis. We next propose a heuristic procedure based on SPE (called SPE(D)) to improve its robustness to SNR levels. We then demonstrate, through simulated physiologic data at high SNR levels, that SPE will be equivalent to consistent model order selection criteria for long data records but will become superior to FPE and other model order selection criteria as the size of the data record decreases. The simulated data results also show that SPE(D) is indeed a significant improvement over SPE in terms of robustness to SNR. Finally, we demonstrate the applicability of SPE and SPE(D) to actual cardio-respiratory-renal data.     

On optimal linear estimation of signals with general spectral distribution (Corresp.)

It is standard practice to assume that second-order stationary signal and noise processes involved in a linear estimation procedure have spectral densities. A heuristic justification may be based on the reasoning that the part of the signal having singular spectral distribution can be precisely determined, and the part of the noise having singular spectral distribution can be completely eliminated. Rigorous phrasing and proof of this claim are given here for the most general case, i.e., where the singular parts of the spectral distributions may contain continuous components, in which situation the intuitive picture is obscure. The discussion includes both discrete-time and continuous-time processes, and the multivariable case is also treated.     

Mode‐SVD‐Based Maximum Likelihood Source Localization Using Subspace Approach

A mode‐singular‐value‐decomposition (SVD) maximum likelihood (ML) estimation procedure is proposed for the source localization problem under an additive measurement error model. In a practical situation, the noise variance is usually unknown. In this paper, we propose an algorithm that does not require the noise covariance matrix as a priori knowledge. In the proposed method, the weight is derived by the inverse of the noise magnitude square in the ML criterion. The performance of the proposed method outperforms that of the existing methods and approximates the Taylor‐series ML and Cramér‐Rao lower bound.     

Maximum likelihood array processing for stochastic coherent sources

Maximum likelihood (ML) estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature. We focus on the equally relevant case of stochastic coherent signals. Explicit large-sample realizations are derived for the ML estimates of the noise power and the (singular) signal covariance matrix. The asymptotic properties of the estimates are examined, and some numerical examples are provided. In addition, we show the surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ML estimates obtained by exploiting the coherent source information. Thus, the ML signal parameter estimator derived for the noncoherent case (or its large-sample realizations) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound)     

Zero-crossing based spectral analysis and SVD spectral analysis forformant frequency estimation in noise

The authors discuss a method for spectral analysis of noise corrupted signals using statistical properties of the zero-crossing intervals. It is shown that an initial stage of filter-bank analysis is effective for achieving noise robustness. The technique is compared with currently popular spectral analysis techniques based on singular value decomposition and is found to provide generally better resolution and lower variance at low signal to noise ratios (SNRs). These techniques, along with three established methods and three variations of these method, are further evaluated for their effectiveness for formant frequency estimation of noise corrupted speech. The theoretical results predict and experimental results confirm that the zero-crossing method performs well for estimating low frequencies and hence for first formant frequency estimation in speech at high noise levels (~0 dB SNR). Otherwise, J.A. Cadzow's high performance method (1983) is found to be a close alternative for reliable spectral estimation. As expected the overall performance of all techniques is found to degrade for speech data. The standard autocorrelation-LPC method is found best for clean speech and all methods deteriorate roughly equally in noise     

信噪比盲估计算法性能比较

为了实现非协作环境下的通信信号信噪比估计,本文在功率谱分析的基础上,提出了一种基于功率谱差分的信噪比盲估计算法,并将其与传统的基于奇异值分解的信噪比盲估计算法进行了比较。理论与仿真结果表明,与传统方法相比,本文提出的算法不但复杂度低,而且在低信噪比情形下仍具有较高的估计精确度和稳健性。     

随机噪声信号的功率谱估计的仿真

在通讯与电子信息工程行业及领域中,大部分问题的解决需要进行估计一个随机信号在频率域上的功率谱分布,诸如此类的问题有很多,比如：设计滤波器消除噪声信号,振动随机信号的回波抵消,随机信号的特征抽取与表示等等。功率谱估计的分类：一般分为两大类,一类是参数法功率谱估计,一类是非参数法功率谱估计。参数法功率谱估计通常对数据进行一种建模,比如把数据建模成滑动平均模型（Moving Average）,或者自回归（Autoregressive）模型,而非参数法功率谱估计。除了要求信号满足广义平稳之外,不需要其它的统计假设。与非参数法相比较,参数法的优点是在一个给定的数据集合上能够有较少的误差、偏差与方差。     

A theory of adaptive filtering

This paper considers the adaptive signal extraction problem for time-discrete data when only very general a priori assumptions regarding the distributions of signal and noise are possible. Specifically, it is assumed that the noise is white, additive, and signal independent with mean zero and unknown variance and that the signal is band-limited. No stationarity assumptions are required. After a procedure is found under these conditions, the mean-square-error is derived asymptotically under narrower conditions-stationary Gaussian data with mean zero. Finally, a method of estimating the error variance from the data (without knowing the signal directly) is found.     

LMS-like AR modeling in the case of missing observations

This paper presents a new recursive algorithm for the time domain reconstruction and spectral estimation of uniformly sampled signals with missing observations. An autoregressive (AR) modeling approach is adopted. The AR parameters are estimated by optimizing a mean-square error criterion. The optimum is reached by means of a gradient method adapted to the nonperiodic sampling. The time-domain reconstruction is based on the signal prediction using the estimated model. The power spectral density is obtained using the estimated AR parameters. The development of the different steps of the algorithm is discussed in detail, and several examples are presented to demonstrate the practical results that can be obtained. The spectral estimates are compared with those obtained by known AR estimators applied to the same signals sampled periodically. We note that this algorithm can also be used in the case of nonstationary signals     

不同相位噪声谱对QPSK的性能影响分析

研究了相位噪声对QPSK系统的性能影响,利用高斯信道下带有相位噪声的条件误码率公式,分析了不同相位噪声谱所带来的解调损失。相位调制是一种恒包络调制方式,它对调制信号的相位偏移非常敏感,在单频相位噪声模型基础上,把相位噪声功率谱密度与相干解调的误码率公式相联系起来,计算了高斯信道条件下不同相位噪声谱对不同速率QPSK信号的解调损失。     

On rates of convergence of general information criteria in signalprocessing when the noise covariance matrix is arbitrary

The authors give exponential-type bounds on the probabilities of detection error under certain conditions. The bounds tend to zero rapidly as the sample size increases. These procedures are referred to as general information criterion (GIC) procedures since each is consistent and, under certain conditions, the rate of convergence of the estimate of the number of signals to the true value is rapid. The authors give bounds on the probability of wrong detection of the GIC procedure when the noise variance is unknown. Upper bounds on the probabilities of detection error are also obtained     

Perturbation-Based Eigenvector Updates for On-Line Principal Components Analysis and Canonical Correlation Analysis

Principal components analysis is an important and well-studied subject in statistics and signal processing. Several algorithms for solving this problem exist, and could be mostly grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second order statistical criterion (like reconstruction error or output variance), and fixed point update rules with deflation. In this study, we propose an alternate approach that avoids deflation and gradient-search techniques. The proposed method is an on-line procedure based on recursively updating the eigenvector and eigenvalue matrices with every new sample such that the estimates approximately track their true values as would be calculated analytically from the current sample estimate of the data covariance matrix. The perturbation technique is theoretically shown to be applicable for recursive canonical correlation analysis, as well. The performance of this algorithm is compared with that of a structurally similar matrix perturbation-based method and also with a few other traditional methods like Sanger’s rule and APEX.

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Optimal pyramidal decomposition for progressive multidimensionalsignal coding using optimal quantizers

Optimal hierarchical coding is sought, for progressive or scalable multidimensional signal transmission, by minimizing the variance of the error difference between the original image and its lower resolution renditions. The optimal, according to the above criterion, pyramidal coders are determined for images quantized using the optimal vector Lloyd-Max quantizers. A rigorous general statistical model of a vector Lloyd-Max quantizer is used, consisting of a linear time-invariant filter followed by additive noise uncorrelated with the input. Given arbitrary analysis filters, the optimal synthesis filters are found. The optimal analysis filters are subsequently determined, leading to formulas for globally optimal structures for pyramidal multidimensional signal decompositions. These structures produce replicas of the original image, which at lower resolutions retain as much similarity to the original as possible. This is highly useful for the progressive coding of two- or three-dimensional (2-D or 3-D) images needed in applications such as fast browsing through image databases. Furthermore, the minimization of the variance of the error image leads to minimization of the variance of the quantization noise for this image and, hence, to its optimally efficient compression. Experimental results illustrate the implementation and performance of the optimal pyramids in application for the coding of still 2-D images     

Perfect sampling for the wavelet reconstruction of signals

The coupling from the past (CFTP) procedure is a protocol for finite-state Markov chain Monte Carlo (MCMC) methods whereby the algorithm itself can determine the necessary runtime to convergence. In this paper, we demonstrate how this protocol can be applied to the problem of signal reconstruction using Bayesian wavelet analysis where the dimensionality of the wavelet basis set is unknown, and the observations are distorted by Gaussian white noise of unknown variance. MCMC simulation is used to account for model uncertainty by drawing samples of wavelet bases for approximating integrals (or summations) on the model space that are either too complex or too computationally demanding to perform analytically. We extend the CFTP protocol by making use of the central limit theorem to show how the algorithm can also monitor its own approximation error induced by MCMC. In this way, we can assess the number of MCMC samples needed to approximate the integral to within a user specified tolerance level. Hence, the method automatically ensures convergence and determines the necessary number of iterations needed to meet the error criteria     

Optimal construction of subband coders using Lloyd-Max quantizers

A new method is presented for the analysis of the effects of Lloyd-Max quantization in subband filterbanks and for the optimal design of such filterbanks. A rigorous statistical model of a vector Lloyd-Max quantizer is established first, consisting of a linear time-invariant filter followed by additive noise uncorrelated/with the input. On the basis of this model, an expression for this variance of the error of a subband coder using Lloyd-Max quantizers is explicitly determined. Given analysis filters that statistically separate the subbands, it is shown that this variance is minimized if the synthesis filters are chosen, which mould achieve perfect reconstruction in lossless coding. The globally optimum of such a filterbank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. An alternative design method is also evaluated and optimized. In this, the errors correlated with the signal are set to zero, leaving a random error residue uncorrelated with the signal. This design method is optimized by choosing the analysis filters so as to minimize the random error variance. The results are evaluated experimentally in the realistic setting of a logarithmically split subband image coding scheme.     

Synthetic instruments extract masked signal parameters

We have reviewed the signal conditioning required to obtain high-quality spectral measurements with an FFT-based spectrum analyzer. The conditioning includes data windowing and extended length. Folded windows are required at the input to the transform, and significant ensemble averaging of power spectrum and cross power spectrum at the output of the FFT is needed. We also commented on the effect of cross coupling between signal and noise terms on the variance of the spectral output terms when the signal contains both spectral lines and additive noise. Finally, we presented techniques based on cross spectra. In particular, the normalized cross spectra known as the coherence function was shown as a technique to separate spectral components traceable to the input signal from those not traceable to the input signal.     

基于卡尔曼滤波的压缩感知弱匹配去噪重构

现有的贪婪迭代类压缩感知重构算法均基于最小二乘对信号进行波形估计,未考虑到可能将量测噪声引入信号估计的情况.针对以上不足,提出了一种基于线性Kalman滤波的压缩感知弱匹配去噪重构算法.该算法不需已知稀疏度先验,通过引入Kalman滤波,在最小均方误差准则下,每次迭代都获得最佳信号估计;并以弱匹配的方式同时筛选出有效的原子,并剔除冗余原子进而重构原信号.新算法继承了现有贪婪迭代类算法的有效性,同时避免了因噪声干扰或稀疏度未知导致的重构失败.理论分析和实验表明,新算法在同等条件下,重构性能优于现有典型贪婪迭代类算法,且其运算时间低于BPDN算法和同类的KFCS算法.     

DOA估计算法评价准则在不同功率入射信号下的修正

针对复杂电磁环境中信号功率对入射信号波达方向（DOA）估计的影响问题进行研究,发现用于DOA估计算法性能分析的经典评价准则对不同功率入射信号存在局限性。针对该问题,首先证明了强信号功率会影响弱信号DOA估计性能,得到强信号功率增加会导致弱信号功率克拉美罗界上升,即弱信号DOA估计的均方根误差增加。然后分析了DOA估计算法的经典评价准则对分辨不同功率入射信号存在的局限性,通过蒙特卡洛实验验证了经典评价准则对分辨不同功率入射信号存在较大误判率,当弱信号信噪比低于5dB时,其误判率大于50%。最后本文提出了DOA估计算法新的评价准则,并仿真证明了新准则较经典准则更适用于分辨弱信号信噪比较低时的不同功率入射信号。所提出的评价准则可为基于空间谱估计的DOA估计算法性能分析提供参考依据。      

Mathematical modeling and spectrum analysis of the physiologicalpatello-femoral pulse train produced by slow knee movement

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal.(ABSTRACT TRUNCATED AT 250 WORDS)     

利用奇异谱分析的深度神经网络语音增强方法

针对现有深度神经网络语音增强方法对带噪语音的去噪能力有限、语音质量提升不高的问题，提出了一种基于奇异谱分析的深度神经网络语音增强方法。通过引入奇异谱分析算法对带噪语音进行预处理，以初步分离得到语音信号与噪声。接着将语音信号与噪声用于深度神经网络模型得训练，以得到性能更优的网络模型，从而使得本文方法具有更好的性能。最后在重建干净语音的环节中，同时使用神经网络估计得到的对数功率谱和带噪语音的对数功率谱，并加入了权重系数，使得本文提出的方法可以适应不同信噪比的情形，有效的去除背景噪声，降低语音信号的失真。本文通过仿真实验验证了该方法的有效性和鲁棒性。