Deterministic Signals Research Articles

Can stochastic resonance and coherence resonance describe CDW dynamics in quasi-one dimensional conductors?

Stochastic resonance (SR) in nonlinear systems is a counterintuitive concept in which a weak periodic signal and noise cooperate and give rise to a maximum in the signal-to-noise ratio at the output of the system when the noise is tuned to a certain value. In the coherence resonance phenomenon (CR), there is no deterministic signal to be enhanced. Intrinsic oscillations are present as transients. Adding an optimum noise turns transients into coherent ones. We discuss the possible application of SR and CR concepts to CDW dynamics in quasi-one dimensional conductors. We show in a preliminary experiment that addition of white noise can modify the behavior of the CDW in the quasi-one dimensional conductor K0.30MoO3.

Output Regulation in Discrete‐Time Switched Bimodal Systems Based on Youla Parameterized Stabilizing Controllers

Motivated by a class of contact vibration control problems in mechanical systems, this paper considers a regulation problem for discrete‐time switched bimodal linear systems where it is desired to achieve output regulation against partially known deterministic and unknown random exogenous signals. First, a set of observer‐based Youla parameterized stabilizing controllers is constructed, based on which the regulation conditions for the switched system against the deterministic signals along with an H2 performance constraint against the unknown random signals are derived. Then a corresponding regulator synthesis algorithm is developed based on solving properly formulated linear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence, demonstrating the effectiveness of the proposed regulation approach.

MLICA-Based Separation Algorithm for Complex Sinusoidal Signals with PDF Parameter Optimization

Blind source separation (BSS) techniques are required for various signal decomposing issues. Independent component analysis (ICA), assuming only a statistical independence among stochastic source signals, is one of the most useful BSS tools because it does not need a priori information on each source. However, there are many requirements for decomposing multiple deterministic signals such as complex sinusoidal signals with different frequencies. These requirements may include pulse compression or clutter rejection. It has been theoretically shown that an ICA algorithm based on maximizing non-Gaussianity successfully decomposes such deterministic signals. However, this ICA algorithm does not maintain a sufficient separation performance when the frequency difference of the sinusoidal waves becomes less than a nominal frequency resolution. To solve this problem, this paper proposes a super-resolution algorithm for complex sinusoidal signals by extending the maximum likelihood ICA, where the probability density function (PDF) of a complex sinusoidal signal is exploited as a priori knowledge, in which the PDF of the signal amplitude is approximated as a Gaussian distribution with an extremely small standard deviation. Furthermore, we introduce an optimization process for this standard deviation to avoid divergence in updating the reconstruction matrix. Numerical simulations verify that our proposed algorithm remarkably enhances the separation performance compared to the conventional one, and accomplishes a super-resolution separation even in noisy situations. key words: radar signal processing, maximum likelihood independent component analysis (MLICA), complex sinusoidal signals, PDF parameter optimization

Convergence vector of normalized least-mean-square algorithm for predicting deterministic sinusoidal signals

Convergence vector of normalized least-mean-square algorithm for predicting deterministic sinusoidal signals

Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the probabilistic CS and deterministic sensor array signal processing has not been fully understood. The main contribution of the present article is a unified approach that revisits the link between CS and array signal processing first unveiled in the mid 1990s by Feng and Bresler. The new algorithm, which we call compressive MUSIC, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and that it can approach the optimal -bound with finite number of snapshots even in cases where the signals are linearly dependent.

A Novel Multi-Scale Modeling Approach to Infer Whole Genome Divergence

We propose a novel and simple approach to elucidate genomic patterns of divergence using principal component analysis (PCA). We applied this methodology to the metric space generated by M. musculus genome-wide SNPs. Distance profiles were computed between M. musculus and its closely related species, M. spretus, which was used as external reference. While the speciation dynamics were apparent in the first principal component, the within M. musculus differentiation dimensions gave rise to three minor components. We were unable to obtain a clear divergence signature discriminating laboratory strains, suggesting a stronger effect of genetic drift. These results were at odds with wild strains which exhibit defined deterministic signals of divergence. Finally, we were able to rank novel and previously known genes according to their likelihood to be under selective pressure. In conclusion, we posit PCA as a robust methodology to unravel diverging DNA regions without any a priori forcing.

Detection with the scan and the average likelihood ratio

We investigate the performance of the scan (the maximum likelihood ra- tio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate sampled data model with white Gaussian noise. Our results show that the scan statistic, a popular tool for detection problems, is optimal only for the detection of signals with the smallest spatial extent. For signals with larger spatial extent the scan is suboptimal, and the power loss can be considerable. In contrast, the average likelihood ratio statistic is optimal for the detection of signals on all scales except the smallest ones, where its performance is only slightly suboptimal. We give rigorous mathematical statements of these results as well as heuristic explana- tions that suggest that the essence of these findings applies to detection problems quite generally, such as the detection of clusters in models involving densities or intensities, or the detection of multivariate signals. We present a modification of the average likelihood ratio that yields optimal detection of signals with arbitrary extent and which has the additional benefit of allowing for a fast computation of the statistic. In contrast, optimal detection with the scan seems to require the use of scale-dependent critical values.

Signaling in deterministic and stochastic settings

We contrast a standard deterministic signaling game with one where the signal-generating mechanism is stochastic. With stochastic signals a unique equilibrium emerges that involves separation and has intuitive comparative-static properties as the degree of signaling depends on the prior type distribution. With deterministic signals both pooling and separating configurations occur. Laboratory data support the theory: in the stochastic variant, there is more signaling behavior than with deterministic signals, and less frequent types distort their signals relatively more. Moreover, the degree of congruence between equilibrium and subject behavior is greater in stochastic settings compared to deterministic treatments.

Behavior Analysis of FxLMS Based on Deterministic Signal

In active vibration control, most of the signals to be eliminated are deterministic signals. Simulations are carried out using periodic sinusoidal reference signal based on FxLMS algorithm. Based on a deterministic reference signal input conditions, the paper provides a detailed behavior analysis due to the secondary-path model error and phase delay, the results will give theoretical basis by adjusting the FxLMS algorithm parameters to ensure convergence and to achieve the best control performance in practical applications.

Maximum Likelihood Direction-of-Arrival Estimation of Underwater Acoustic Signals Containing Sinusoidal and Random Components

We consider the problem of maximum-likelihood (ML) direction-of-arrival (DOA) estimation of underwater acoustic signals from ships, submarines, or torpedoes, which contain both sinusoidal and random components, and are called mixed signals in this paper. We model the mixed signals as the mixture of deterministic sinusoidal signals and stochastic Gaussian signals, and derive the ML DOA estimator for the mixed signals under spatially white noise. We compute the asymptotic error covariance matrix of the proposed ML estimator, as well as that of the typical stochastic estimator assuming zero-mean Gaussian signals, for DOA estimation of mixed signals. Our analytical comparison and numerical examples show that the proposed ML estimator, which takes advantage of the sinusoidal components in the mixed signals, improves the DOA estimation accuracy for the mixed signals compared with the typical stochastic estimator assuming zero-mean Gaussian signals.

Extraction of angle deterministic signals in the presence of stationary speed fluctuations with cyclostationary blind source separation

This paper addresses the use of a cyclostationary blind source separation algorithm (namely RRCR) to extract angle deterministic signals from mechanical rotating machines in presence of stationary speed fluctuations. This means that only phase fluctuations while machine is running in steady-state conditions are considered while run-up or run-down speed variations are not taken into account. The machine is also supposed to run in idle conditions so non-stationary phenomena due to the load are not considered. It is theoretically assessed that in such operating conditions the deterministic (periodic) signal in the angle domain becomes cyclostationary at first and second orders in the time domain. This fact justifies the use of the RRCR algorithm, which is able to directly extract the angle deterministic signal from the time domain without performing any kind of interpolation. This is particularly valuable when angular resampling fails because of uncontrolled speed fluctuations. The capability of the proposed approach is verified by means of simulated and actual vibration signals captured on a pneumatic screwdriver handle. In this particular case not only the extraction of the angle deterministic part can be performed but also the separation of the main sources of excitation (i.e. motor shaft imbalance, epyciloidal gear meshing and air pressure forces) affecting the user hand during operations.

On Causal Estimation From Bandlimited Stationary Sequences

This paper considers the problem of estimating a stationary sequence y from the observation of a stationary correlated sequence x by means of a causal linear filter. Thereby, it is assumed that the spectral density Φx of x vanishes on a subset of the unit circle of positive Lebesgue measure such that the classical derivation of the estimation filter, based on the spectral factorization of Φx, can not be applied. The paper derives the transfer function of such an estimation filter, discusses its stability behavior, and applies the result to the causal reconstruction of deterministic signals from its samples.

Maximum Likelihood Estimator Under a Misspecified Model With High Signal-to-Noise Ratio

It is well known that the maximum-likelihood estimator (MLE) under a misspecified model converges to a well defined limit and it is asymptotically Gaussian as the sample size goes to infinity. In this correspondence, we consider a misspecified model with deterministic signal embedded in Gaussian noise and fully characterize the asymptotic performance of the MLE under this misspecified model with high signal-to-noise (SNR). We see that under some regularity conditions, it converges to a well defined limit and is asymptotically Gaussian with high SNR.

Phase Modulated Waveforms for Transponder-Based Radar Sensing: Signal Optimization and Experiments

Both the theoretical and engineering aspects of using transponder-based signal waveforms, such as pulse-position-modulated 1090-MHz Automatic Dependent Surveillance-Broadcast, for noncooperative target sensing are discussed in this article. The random binary phase modulation coding technique is applied to the original transponder signal waveforms to improve the autocorrelation and sidelobe performance. A detailed study of the characterizations of this waveform and its potential for target detection is presented. The impact of random phase coding is analyzed from both signal spectrum (based on stochastic signal model) and radar ambiguity functions (based on deterministic signal model). The combination of pulse-position modulation and maximum length binary random phase coding sequence is shown to have satisfactory performance. In terms of optimal receiver, the traditional correlation receiver (or matched filter) and mismatched filters with different criteria are analyzed. The tradeoffs of receiver design for transponder-based radars are discussed. The experimental implementation of a transponder-based radar sensor with arbitrary waveform generator and commercial, off-the-shelf components is introduced and discussed. The experiment results show that noncooperative target detection using such a radar sensor is feasible with appropriate design of waveforms, system architecture and signal processors.

A comparison of methods for separation of deterministic and random signals

A comparison of methods for separation of deterministic and random signals

Near-Optimal Deterministic Filtering on the Rotation Group

This technical note considers the problem of obtaining minimum-energy state estimates for a system defined on the rotation group, . The signals of the system are modeled as purely deterministic signals. We derive a nonlinear observer (“filter”) posed directly on that respects the geometry of the group and achieves a performance that is close to optimal in the sense of minimizing an integral cost that is measuring the state energy. The performance of the proposed filter is demonstrated in simulations involving large initialization, process and measurement errors where the results are compared against a quaternion implementation of an Extended Kalman Filter. Our results indicate that the proposed filter achieves better robustness against a range of noise levels and initialization errors.

H ∞ filtering for uncertain stochastic systems subject to sensor nonlinearities

This work considers the filtering problem for uncertain stochastic systems subject to sensor nonlinearities. It may be seen from simulation results in this work that the traditional filtering method based on linear measurement may not provide a reliable solution to this problem due to the existence of the nonlinear characteristic of sensors. In the system under consideration, there exist time-varying parameter uncertainties, and state and external-disturbance-dependent noise. Robust filters are constructed for both continuous and discrete stochastic systems, such that the resultant filtering error systems are robustly stochastically stable with a prescribed H ∞-disturbance attenuation performance. Finally, some simulation results with deterministic or stochastic disturbance signals are given to illustrate the proposed method.

Sampling of Deterministic Signals and Systems

In this paper, we analyze sampling approximations of stable linear time-invariant systems for input signals in the Paley-Wiener space <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PW</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . The goal is to approximate a transform <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tf</i> by using only the samples of the signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> , which do not necessarily have to be equidistant. We completely characterize the stable linear time-invariant (LTI) systems <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> and sampling patterns for which the approximation process converges to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tf</i> for all signals in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PW</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . Furthermore, we prove that for every complete interpolating sequence there exist a stable LTI system and a signal in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PW</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> for which the approximation error increases unboundedly as the number of samples that are used for the approximation is increased. This shows that a more flexible choice of the sampling points instead of equidistant sampling, where such a divergence behavior is known to exist, is not sufficient to overcome the divergence. Thus, sampling based signal processing has fundamental limits. The calculations further indicate that oversampling cannot resolve the convergence problems.

U-Invariant Sampling: Extrapolation and Causal Interpolation From Generalized Samples

Causal processing of a signal's samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problems of predicting future samples and causally interpolating deterministic signals. We treat a rich variety of sampling mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an antialiasing filter and magnetic resonance imaging (MRI), which correspond respectively to the translation and modulation operators. From an abstract Hilbert-space viewpoint, such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, although our problems are deterministic by nature. In particular, we provide necessary and sufficient conditions on the sampling mechanism such that perfect prediction is possible. For cases where perfect prediction is impossible, we derive the predictor minimizing the prediction error. We also derive a causal interpolation method that best approximates the commonly used noncausal solution. Finally, we study when causal processing of the samples of a signal can be performed in a stable manner.

Analysis of an Adaptive Sampler Based on Weber's Law

Weber's law suggests a logarithmic relationship between perceptual stimuli and human perception. The Weber sampler is an adaptive, nonuniform sampling mechanism that exploits Weber's law to sample the signal at a minimum rate without significant perceptual degradation. In this paper, we introduce and analyze a regularized Weber sampler for smooth deterministic signals as well as smooth random processes. While analysis for a fixed Weber constant δ is analytically intractable except for some special cases, we exploit the fact that the Weber constant is usually small. Under suitable assumptions, for deterministic signals, we provide analytical approximations to the number of samples in a unit time interval and the intersample times. For a random signal, we give analytical approximations to the expectation and probability distribution function of the respective quantities. Our class of deterministic as well as random signals is quite wide, and in particular covers bandlimited signals and signals satisfying second order ordinary differential equations. We also present a number of simulations to demonstrate that our approximations are good up to a Weber constant of 0.2, which is the regime of practical interest. Our results provide a source model for the Weber sampler, which can be used in the study of transmission of perceptual stimuli signals over communication links.