Signals In White Gaussian Noise Research Articles

Semiparametric shift estimation based on the cumulated periodogram for non-regular functions

The problem of estimating the center of symmetry of a symmetric signal in Gaussian white noise is considered. The underlying nuisance function f is not assumed to be differentiable, which makes a new point of view to the problem necessary. We investigate the well-known sieve maximum likelihood estimators based on the cumulated periodogram, and study minimax rates over classes of irregular functions. It is shown that if the class appropriately controls the growth to infinity of the Fisher information over the sieve, semiparametric fast rates of convergence are obtained. We prove a lower bound result which implies that these semiparametric rates are really slower than the parametric ones, contrary to the regular case. Our results also suggest that there may be room to improve on the popular cumulated periodogram estimator.

Nonparametric detection of frequency modulated signals using fractional Fourier transform

A detection scheme for unknown nonlinear frequency modulated signals in white Gaussian noise is developed using the fractional Fourier transform and two-dimensional order-statistic filter. The simulation experiment and comparison with other methods available are shown, and the effectiveness of the proposed method is reported.

Frequency-Domain Correlation: An Asymptotically Optimum Approximation of Quadratic Likelihood Ratio Detectors

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.

The application of particle filters in single trial event-related potential estimation

In this paper, an approach for the estimation of single trial event-related potentials (ST-ERPs) using particle filters (PFs) is presented. The method is based on recursive Bayesian mean square estimation of ERP wavelet coefficients using their previous estimates as prior information. To enable a performance evaluation of the approach in the Gaussian and non-Gaussian distributed noise conditions, we added Gaussian white noise (GWN) and real electroencephalogram (EEG) signals recorded during rest to the simulated ERPs. The results were compared to that of the Kalman filtering (KF) approach demonstrating the robustness of the PF over the KF to the added GWN noise. The proposed method also outperforms the KF when the assumption about the Gaussianity of the noise is violated. We also applied this technique to real EEG potentials recorded in an odd-ball paradigm and investigated the correlation between the amplitude and the latency of the estimated ERP components. Unlike the KF method, for the PF there was a statistically significant negative correlation between amplitude and latency of the estimated ERPs, matching previous neurophysiological findingsSome preliminary results of this work were presented in Mohseni et al (2008b Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP) pp 465–68)..

Critical ratios in harbor porpoises (Phocoena phocoena) for tonal signals between 0.315 and 150 kHz in random Gaussian white noise

A psychoacoustic behavioral technique was used to determine the critical ratios (CRs) of two harbor porpoises for tonal signals with frequencies between 0.315 and 150 kHz, in random Gaussian white noise. The masked 50% detection hearing thresholds were measured using a "go/no-go" response paradigm and an up-down staircase psychometric method. CRs were determined at one masking noise level for each test frequency and were similar in both animals. For signals between 0.315 and 4 kHz, the CRs were relatively constant at around 18 dB. Between 4 and 150 kHz the CR increased gradually from 18 to 39 dB ( approximately 3.3 dB/octave). Generally harbor porpoises can detect tonal signals in Gaussian white noise slightly better than most odontocetes tested so far. By combining the mean CRs found in the present study with the spectrum level of the background noise levels at sea, the basic audiogram, and the directivity index, the detection threshold levels of harbor porpoises for tonal signals in various sea states can be calculated.

A stochastic dynamic controller for random early detection queues using a Kalman filter algorithm

AbstractThe stabilizing random early detection (RED) congestion control algorithm in transmission control protocol (TCP)/IP networks is a control theory problem. Significant attention has been drawn to this problem in the networking and control theory research communities. In this paper, we use a nonlinear dynamic model of the TCP RED congestion control algorithm to analyze and design active queue management (AQM) control systems. A linearized model of RED behavior around its nominal operating point which implicitly includes the delay in the control signal is derived. It is assumed that the system model is corrupted at the input and output by zero mean white Gaussian noise signals. An optimal state feedback stochastic controller is designed for the linearized model of the system in conjunction with a Kalman filter for state estimation. To illustrate the proposed design methodology, simulations results are presented and discussed. The proposed stochastic controller is applied to the nonlinear model of the system; Simulation results indicate that the proposed controller keeps the queue length bounded in an appropriate stochastic sense. Copyright © 2009 John Wiley & Sons, Ltd.

Adaptive filtering of a random signal in Gaussian white noise

We consider the problem of estimating an infinite-dimensional vector ? observed in Gaussian white noise. Under the condition that components of the vector have a Gaussian prior distribution that depends on an unknown parameter β, we construct an adaptive estimator with respect to β. The proposed method of estimation is based on the empirical Bayes approach.

Matched Subspace Detection With Hypothesis Dependent Noise Power

We consider the problem of detecting a subspace signal in white Gaussian noise when the noise power may be different under the null hypothesis - where it is assumed to be known - and the alternative hypothesis. This situation occurs when the presence of the signal of interest (SOI) triggers an increase in the noise power. Accordingly, it may be relevant in the case of a mismatch between the actual SOI subspace and its presumed value, resulting in a modelling error. We derive the generalized likelihood ratio test (GLRT) for the problem at hand and contrast it with the GLRT which assumes known and equal noise power under the two hypotheses. A performance analysis is carried out and the distributions of the two test statistics are derived. From this analysis, we discuss the differences between the two detectors and provide explanations for the improved performance of the new detector. Numerical simulations attest to the validity of the analysis.

대역 확장을 통한 MP3 오디오의 음질 향상

In this paper, we investigate methods to enhance the perceptual quality of MP3-coded audios. Based on the high frequency reconstruction method by Liu, in the proposed method, we determine adaptively the starting point of high frequency reconstruction. We also present an improved linear estimation method. For high frequency component generation, we compare two methods. One is a replication of low-frequency components and the other is an insertion of additive white Gaussian noise signals. Through subjective tests, we shall show that the proposed method can improve the perceptual quality of MP3-coded audio.

Mining information from binary black hole mergers: A comparison of estimation methods for complex exponentials in noise

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, nonlinear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole's rotation, if the radiation field is expanded in terms of spin-weighted spherical harmonics (rather than spin-weighted spheroidal harmonics). Observing deviations from the predictions of linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by numerical error. So far, nonlinear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using ``test'' damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard nonlinear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for nonlinearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).

Simulating the effect binaural (electric and acoustic) hearing on Mandarin speech recognition under background noise for patients with cochlear implant (CI)

This study evaluated the effects of binaurally combined electric and acoustic hearing on Mandarin speech recognition under simulated background noise for normal‐hearing (NH) listeners and CI recipients of the Nucleus‐24 device with contralateral hearing aid (HA). Chinese word and tone recognition were measured in seven NH subjects using simulated four‐channel continuous interleaved sampler (CIS) type speech processing strategy under three different conditions, namely, (1) only simulated (CI) signals with modulated Gaussian white noise for monaural stimulation, (2) simulated (CI) signals with modulated Gaussian white noise and simulated HA signals (low‐pass speech signals with cutoff frequency of 500 Hz) for monaural stimulation, and (3) simulated (CI) signals with modulated Gaussian white noise to one ear and simulated hearing aid (HA) signals to the other ear for dichotic stimulation. For comparison purposes, Chinese word and tone recognition were also measured in three CI users using advanced combination encoding (ACE) strategy. Preliminary results showed that the Chinese word and tone recognition rates of the NH listeners and CI recipients are statistically significantly improved (word and tone recognition rates were improved from 3.85% to 60.86% and 40.14% to 97.43% for NH listeners and 20% to 37.5% and 50% to 90% for CI recipients).

Optimum time–frequency distribution for detecting a discrete-time chirp signal in noise

In the continuous-time domain, maximum-likelihood (ML) detection of a chirp signal in white Gaussian noise can be done by maximising (with respect to signal parameter arguments) the line-integral transform (LIT) of the classical Wigner distribution (of the observed signal). The LIT is known variously as the Hough transform and the Radon transform. For discrete-time signals, the Wigner-type distribution defined by Claasen and Mecklenbrauker has become popular as a signal analysis tool. Moreover, it is commonly believed that ML detection of a discrete-time chirp signal in independent and identically distributed (i.i.d.) Gaussian noise can be done by maximising the LIT of the Wigner–Claasen–Mecklenbrauker distribution (WCMD). This belief is false and results in loss of performance. The authors derive a Wigner-type distribution for discrete-time signals such that ML detection of a discrete-time chirp signal in i.i.d. Gaussian noise can be done by maximising the LIT of this distribution. Simulated receiver operating curves showing the performance advantage of the new method over the WCMD-based method are provided. The signal parameter values that maximise the LIT are taken as estimates of the actual parameters. The authors provide simulation results showing that the parameter estimates obtained using the new method are more accurate than those obtained using the WCMD-based method. For the WCMD-based method, the range of unambiguously measurable frequencies (RUMF) is [−π/2, π/2]. For the new method, the RUMF is [−π, π].

A computationally efficient technique for estimating the parameters of polynomial-phase signals from noisy observations

Many real-world applications are characterized by the presence of polynomial phase signals embedded in noise. These applications include radar, sonar, telemetry, communications, and power systems. In a significant number of these applications, it is highly desirable to be able to accurately estimate the polynomial phase signal parameters. This correspondence presents a computationally efficient method for estimating any or all of the parameters of polynomial-phase signals in white Gaussian noise and provides a first-order statistical analysis of the technique. Simulations are also presented to support the theoretical analysis.

Adaptation of the transfer function of the Hodgkin–Huxley (HH) neuronal model

The transfer functions of sensory neurons are known to adapt to the statistics of the input signals. It is however unclear whether such adaptation arises from the nonlinear dynamics of the neuron or emerges from the collective interaction among neurons embedded in a network. We investigated the Hodgkin–Huxley (HH) neuronal model's response to Gaussian white noise signals of different variances and found that the recovered kernel adapt its preferred temporal frequency and its energy gains according to noise variance. This adaptation is likely a consequence of the cooperative interaction between the noises and the bifurcation dynamics of the neurons.

An eigenvalue residuum-based criterion for detection of the number of sinusoids in white Gaussian noise

It is understood that the eigenvalues of a covariance matrix, deriving from the data of multiple sinusoidal signals in white Gaussian noise, can be divided into two groups when the dimensions of the covariance matrix are larger than the number of sinusoidal signals. One is composed of the sinusoidal signals plus the noise. Another is called ‘small eigenvalues’ which is produced by the noise only. It is also known that the small eigenvalues are an asymptotic Gaussian random process. Based on these facts, an eigenvalue-based residuum criterion for the detection of the number of sinusoids in white Gaussian noise is presented in this paper. Using this criterion, the small eigenvalues of the covariance matrix can gradually be ruled out. While the eigenvalues which belong to the signal and noise are separated, the number of sinusoids is detected successfully. Simulation results exhibit that the proposed method gives a superior performance over the Akaike information criterion (AIC) and the minimum description length principle (MDL), especially for situations where the analyzed signals exhibit a low signal-to-noise ratio (SNR), short data records, and a high number of sinusoids. In addition, the implementation of the new criterion is simpler and faster.

A sharp upper bound for the probability of error of the likelihood ratio test for detecting signals in white Gaussian noise

A new sharp upper bound for the probability of error of the likelihood ratio test is given for the detection in white Gaussian noise of any random vector whose norm is greater than, or equal to, a given value and whose probability of presence is less than, or equal to, one half. Also, a new test for the detection of such vectors is described. This test does not depend on the distribution of the signal vector but nevertheless its probability of error is less than, or equal to, the given upper bound.

Small Noise Asymptotics of the Bayesian Estimator in Nonidentifiable Models

We study the asymptotic behavior of the Bayesian estimator for a deterministic signal in additive Gaussian white noise, in the case where the set of minima of the Kullback–Leibler information is a submanifold of the parameter space. This problem includes as a special case the study of the asymptotic behavior of the nonlinear filter, when the state equation is noise-free, and when the limiting deterministic system is nonobservable. As the noise intensity goes to zero, the posterior probability distribution of the parameter asymptotically concentrates on the submanifold of minima of the Kullback–Leibler information. We give an explicit expression of the limit, and we study the rate of convergence. We apply these results to a practical example where nonidentifiability occurs.

On estimation of time dependent spatial signal in Gaussian white noise

We consider an estimation problem for time dependent spatial signal observed in a presence of additive cylindrical Gaussian white noise of a small intensity ε. Under known a priori smoothness of the signal estimators with asymptotically the best in the mimimax sense risk convergence rate in ε to zero are proposed. Moreover, on-line estimators for the signal and its derivatives in t are also created.

Crack Detection in Metallic Structures Using Broadband Excitation of Acousto-Ultrasonics

This paper reports the application of piezoceramic sensors for crack detection in metallic structures. Rectangular aluminium plates with a crack initiated by spark erosion were used in a simple fatigue experiment. The plates were instrumented with piezoceramic devices bonded in a symmetrical configuration on both sides of the crack. One of the piezoceramics was used as an actuator and excited by a sine sweep and Gaussian white noise signals in order to exploit broadband excitation. The plates were subjected to static and dynamic tensile loading. The growing crack was monitored by the remaining piezoceramic sensors. The experimental data were analyzed using time, frequency and wavelet domain statistical parameters. The results show the potential of the low-frequency broadband excitation for structure-integrated damage detection systems based on acousto-ultrasonics in metallics.

Matched filtering-based estimation of ground elevation using laser altimetry

The authors present a method for determining the time-of-arrival (TOA) of the ground component of a laser altimetry return signal. The proposed method takes advantage of the fact that the ground component or ground return is approximately Gaussian shaped and occurs at the end of the return signal. In particular, the method exploits the well-known result that the TOA of a known signal in white Gaussian noise can be estimated using matched filtering. An important feature of the method is that it addresses the problem of overlap between ground and vegetation returns. Simulations using synthetic data indicate that the proposed method provides excellent estimates and greatly outperforms a conventional method. It is anticipated that the method will be applicable to laser altimetry applications where the ground return can be assumed to have an approximately known shape.