Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN

A complex-valued pipelined recurrent neural network (CPRNN) for nonlinear adaptive prediction of complex nonlinear and nonstationary signals is introduced. This architecture represents an extension of the recently proposed real-valued PRNN of Haykin and Li in 1995. To train the CPRNN, a complex-valued real time recurrent learning (CRTRL) algorithm is first derived for a single recurrent neural network (RNN). This algorithm is shown to be generic and applicable to general signals that have complex domain representations. The CRTRL is then extended to suit the modularity of the CPRNN architecture. Further, to cater to the possibly large dynamics of the input signals, a gradient adaptive amplitude of the nonlinearity within the neurons is introduced to give the adaptive amplitude CRTRL (AACRTRL). A comprehensive analysis of the architecture and associated learning algorithms is undertaken, including the role of the number of nested modules, number of neurons within the modules, and input memory of the CPRNN. Simulations on real-world and synthetic complex data support the proposed architecture and algorithms.     

Block adaptive prediction of colour television signals

A single coefficient block-adaptive predictor is described for encoding of colour television signals. The optimum coefficients were obtained for each block of incoming samples according to the selection of sampling frequency. The results show a reduction in large prediction errors, compared with a nonadaptive predictor, and also improvements in signal/prediction-noise ratio.     

非平稳确定性信号与非平稳随机信号统一分类法的探讨

根据信号通过线性系统可产生新信号的理论,对非平稳确定性信号与非平稳随机信号的统一分类方法进行了深入研究,分别给出格林函数描述的线性时变系统法、调制函数作用于边界稳定线性系统的自激振荡正弦波法、随机输入线性时不变系统与边界稳定的与不稳定的线性系统组合法。这3种分类法便于对非平稳确定性信号与非平稳随机信号进行统一分类研究,并具有比较全面与系统性好的优点。     

Screening of vibroarthrographic signals via adaptive segmentationand linear prediction modeling

This paper proposes a noninvasive method to diagnose chondromalacia patella at its early stages by recording knee vibration signals (also known as vibroarthrographic or VAG signals) over the mid-patella during normal movement. An adaptive segmentation method was developed to segment the nonstationary VAG signals. The least squares modeling method was used to reduce the number of data samples to a few model parameters. Model parameters along with a few clinical parameters and a signal variability parameter were then used as discriminant features for screening VAG signals by applying logistic and discriminant algorithms. The system was trained using ten normal and eight abnormal signals. It correctly screened a separate test set of ten normal and eight abnormal signals except for one normal signal. The proposed method should find use as an alternative technique for diagnosis of knee joint pathology or as a test before arthroscopy or major knee surgery     

Evolutionary periodogram for nonstationary signals

Presents a novel estimator for the time-dependent spectrum of a nonstationary signal. By modeling the signal, at any given frequency, as having a time-varying amplitude accurately represented by an orthonormal basis expansion, the authors are able to compute a minimum mean-squared error estimate of this time-varying amplitude. Repeating the process over all frequencies, they obtain a power distribution as a function of time and frequency that is consistent with the Wold-Cramer evolutionary spectrum. Based on the model assumptions, the authors develop the evolutionary periodogram (EP) for nonstationary signals, an estimator analogous to the periodogram used in the stationary case. They also derive the time-frequency resolution of the new estimator. The approach is free of some of the drawbacks of the bilinear distributions and of the short-time Fourier transform spectral estimates. It is guaranteed to produce nonnegative spectra without the cross-term behavior of the bilinear distributions, and it does not require windowing of data in the time domain. Examples illustrating the new estimator are given     

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     

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.     

An adaptive time-frequency filtering method for nonstationary signals based on the generalized S-transform

Aiming at the serious interference of the cross term existing in the time-frequency(TF) filtering method,an adaptive TF filtering method for nonstationary signals based on the generalized S-transform is proposed.Firstly the time-frequency distribution spectrum of the signal is got by the generalized S-transform,then the clustered energy of the signal on the timefrequency plane is identified by the TF region extraction algorithm,thirdly the TF filtering factor is constructed based on the distribution charact...     

Nonlinear adaptive prediction of speech with a pipelined recurrentneural network

New learning algorithms for an adaptive nonlinear forward predictor that is based on a pipelined recurrent neural network (PRNN) are presented. A computationally efficient gradient descent (GD) learning algorithm, together with a novel extended recursive least squares (ERLS) learning algorithm, are proposed. Simulation studies based on three speech signals that have been made public and are available on the World Wide Web (WWW) are used to test the nonlinear predictor. The gradient descent algorithm is shown to yield poor performance in terms of prediction error gain, whereas consistently improved results are achieved with the ERLS algorithm. The merit of the nonlinear predictor structure is confirmed by yielding approximately 2 dB higher prediction gain than a linear structure predictor that employs the conventional recursive least squares (RLS) algorithm     

Linear interpolation lattice for nonstationary signals

A ladder algorithm for linear interpolation of nonstationary signals is developed. The algorithm is based on the sliding-window least-squares method and can be implemented using a lattice structure. Furthermore, by assuming that the input signal is stationary, the number of parameters required to be calculated is reduced. The lattice structure in the case of stationary input is also presented     

Optimized estimation of moments for nonstationary signals

The behavior of nonstationary moment estimators that are based on linear time-invariant filtering is analyzed. The performance of such estimators is evaluated in terms of their time-averaged variance and time-averaged squared bias. Optimal estimators that minimize a convex combination of bias and variance are derived. The superiority of such optimally weighted filtering over the conventional (exponentially windowed) moment estimation technique is demonstrated by means of a simple example. The same example also serves to illustrate the difficulties encountered when the construction of optimal estimators relies on uncertain prior information, as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed (robust) optimal estimators. We also include a brief discussion of the relevance of the proposed moment estimation technique to identification of linear time-variant systems and to estimation of time-variant spectra     

A blind equalizer for nonstationary discrete-valued signals

Adaptive algorithms are proposed for blind equalization of communication channels. The algorithms explicitly utilize the finite alphabetical set of the input signals and minimize a criterion that depends solely on the alphabetical set. The method is shown to be able to handle nonstationary signals without requiring or estimating their time-varying statistical parameters. Simulation results are presented to test and demonstrate the method     

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.     

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.     

一种非平稳信号的DOA估计方法

利用空时频分布(STFD)矩阵估计非平稳信号DOA的关键是选择合适的时频点。用白化后的接收信号矢量构造STFD矩阵,利用该矩阵迹构造判决量来选择时频图的自项,将选择的自项的STFD矩阵平均,然后运用MUSIC算法来估计DOA。仿真证明:本文的方法可以很清晰的选出非平稳信号的自项,运用该自项点的平均STFD矩阵估计的信号DOA更准确。     

A nonparametric nonstationary procedure for failure prediction

The time between failures is a very useful measurement to analyze reliability models for time-dependent systems. In many cases, the failure-generation process is assumed to be stationary, even though the process changes its statistics as time elapses. This paper presents a new estimation procedure for the probabilities of failures; it is based on estimating time-between-failures. The main characteristics of this procedure are that no probability distribution function is assumed for the failure process, and that the failure process is not assumed to be stationary. The model classifies the failures in Q different types, and estimates the probability of each type of failure s-independently from the others. This method does not use histogram techniques to estimate the probabilities of occurrence of each failure-type; rather it estimates the probabilities directly from the values of the time-instants at which the failures occur. The method assumes quasistationarity only in the interval of time between the last 2 occurrences of the same failure-type. An inherent characteristic of this method is that it assigns different sizes for the time-windows used to estimate the probabilities of each failure-type. For the failure-types with low probability, the estimator uses wide windows, while for those with high probability the estimator uses narrow windows. As an example, the model is applied to software reliability data.     

Multiscale correlation analysis of nonstationary signals containing quasi-periodic fragments

Processing of complex nonstationary signals, in particular, their structuring, is considered. The problem of detection of quasi-periodic fragments and determination of the quasi-periodicity parameters is discussed. A multiscale time-and-time representation of the nonstationary signals is introduced on the basis of the selected distribution of the correlation type, and the characteristic features of the representation are discussed. Fast realizations of algorithms for calculation of distributions are considered, and the types of window functions allowing fast algorithms are determined. Examples of processing and representation of real biological (cardiographic, encephalographic, and voice) signals are presented.     

Nonlinear nonstationary Wiener model of infant EEG seizures

This paper presents the estimation of a nonstationary nonlinear model of seizures in infants based on parallel Wiener structures. The model comprises two parts and is partly derived from the Roessgen et al. seizure model. The first part consists of a nonlinear Wiener model of the pure background activity, and the second part in a nonlinear Wiener model of the pure seizure activity with a time-varying deterministic input signal. The two parts are then combined in a parallel structure. The Wiener model consists of an autoregressive moving average filter followed by a nonlinear shaping function to take into account the non-Gaussian statistical behavior of the data. Model estimation was performed on 64 infants of whom four showed signs of clinical and electrical seizures. Model validation is performed using time-frequency-based entropy distance and shows an averaged improvement of 50% in modeling performance compared with the Roessgen model.