Gaussian Noise Source Research Articles

Phase analysis in delayed systems

We study numerically the phase behaviour in two different arrays of overdamped bistable oscillators coupled unidirectionally, each of them fed by an external source of Gaussian white noise, and driven by an external periodic force.

Optimization of an independent component analysis approach for artifact identification and removal in magnetoencephalographic signals.

To propose a noise reduction procedure for magnetoencephalography (MEG) signals introducing an automatic detection system of artifactual components (ICs) separated by an independent component analysis (ICA) algorithm, and a control cycle on reconstructed cleaned data to recovery part of non-artifactual signals possibly lost by the blind mechanism. The procedure consisted of three main steps: (1) ICA for blind source separation (BSS); (2) automatic detection method of artifactual components, based on statistical and spectral ICs characteristics; (3) control cycle on 'discrepancy,' i.e. on the difference between original data and those reconstructed using only ICs automatically retained. Simulated data were generated as representative mixtures of some common brain frequencies, a source of internal Gaussian noise, power line interference, and two real artifacts (electrocardiogram=ECG, electrooculogram=EOG), with the adjunction of a matrix of Gaussian external noise. Three real data samples were chosen as representative of spontaneous noisy MEG data. In simulated data the proposed set of markers selected three components corresponding to ECG, EOG and the Gaussian internal noise; in real-data examples, the automatic detection system showed a satisfactory performance in detecting artifactual ICs. 'Discrepancy' control cycle was redundant in simulated data, as expected, but it was a significant amelioration in two of the three real-data cases. The proposed automatic detection approach represents a suitable strengthening and simplification of pre-processing data analyses. The proposed 'discrepancy' evaluation, after automatic pruning, seems to be a suitable way to render negligible the risk of loose non-artifactual activity when applying BSS methods to real data. The present noise reduction procedure, including ICA separation phase, automatic artifactual ICs selection and 'discrepancy' control cycle, showed good performances both on simulated and real MEG data. Moreover, application to real signals suggests the procedure to be able to separate different cerebral activity sources, even if characterized by very similar frequency contents.

Stochastic resonant memory storage device.

We show that an extended system operating in the regime of stochastic resonance can act as a short-term memory device. The system under study is a ring of overdamped bistable oscillators coupled directionally, being each also subject to an external source of Gaussian white noise (the noise sources are independent). A single oscillator is driven by an external periodic force, assumed to act only over the time that the signal takes to traverse the whole ring. A traveling wave is then found to be transmitted several times along the ring with a small damping, provided that the driven oscillator operates in a regime close to stochastic resonance. If noise is suppressed from any oscillator of the chain, the traveling wave is immediately damped. The ring is thus found to act as a short-term memory device in which the stored information (one bit, corresponding to the presence or absence of the external driving) is sustained by noise during a characteristic time T(mem).

Implementation of a real-time frequency-selective RF channel simulator using a hybrid DSP-FPGA architecture

A low cost frequency-selective RF channel simulator architecture is explored in this paper. The technique of quadrature amplitude modulation (QAM) by independent low-pass filtered white Gaussian noise sources forms a rational function approximation (RFA) to the desired Doppler spectrum for flat Rayleigh fading. To simulate frequency-selective fading, this QAM/RFA architecture may be extended by combining delayed outputs from multiple flat fading generators. In this paper, the noise shaping filter considered is in the form of an infinite-impulse-response digital filter followed by an interpolator (upsampler) using linear interpolation. The performance requirements are those in the standard channel simulator section of TIA IS-55-A. The system is implemented almost entirely in the digital domain by use of IF sampling, with the signal processing performed in a high-end floating-point digital signal processor and a field-programmable gate array. The theoretical performance of the simulator is studied with respect to the TIA standard, and limitations of the hardware prototype are identified. A system capable of simulating 12 delay taps, with a processing bandwidth of 5 MHz, can be built at about one-tenth the cost of commercially available channel simulators of comparable performance.

Resonant bistable flows driven by colored noise

The escape times of an overdamped Brownian particle confined to a quartic bistable potential is known to be extremely sensitive to the fluctuation correlation time. In the presence of an external Gaussian noise source with fixed variance, the escape times develop a minimum for a certain value of the correlation time—a behavior reminiscent of the so-called resonant activation phenomenon. The optimal escape conditions are investigated for a wide range of the noise variance.

Resonant bistable flows driven by colored noise

AbstractThe escape times of an overdamped Brownian particle confined to a quartic bistable potential is known to be extremely sensitive to the fluctuation correlation time. In the presence of an external Gaussian noise source with fixed variance, the escape times develop a minimum for a certain value of the correlation time—a behavior reminiscent of the so‐called resonant activation phenomenon. The optimal escape conditions are investigated for a wide range of the noise variance.

Quantitative evaluation of techniques for ocular artefact filtering of EEG waveforms

The electrical dipoles of eyes change by eye movements and blinks, producing a signal known as an electrooculogram (EOG). A fraction of EOGs contaminate the electrical activity of the brain (electroencephalogram, EEG), Ocular artefact (OA) is a collective term used to represent EEG contaminating potentials caused by eye movements and blinks. A procedure for quantifying the effectiveness of an algorithm for removing OA from the EEG was devised. This enabled the similarity between the EEG waveforms before contamination by OA and the contaminated EEG waveforms following their processing by an OA removal method to be measured. Four methods for OA removal were included in the study: extended independent component analysis (ICA), joint approximation diagonalisation of eigenmatrices (JADE), principal component analysis (PCA) and EOG subtraction. The operation of JADE and ICA is subject to amplitude scaling and channel permutation. Procedures were incorporated to estimate the amplitude of the recovered EEG waveforms and to allocate them to the correct channels. It was demonstrated that the signal separation techniques of JADE and extended ICA were more effective than EOG subtraction and PCA for removing OA from the EEG. EOG subtraction was shown to cause attenuation of the recovered EEG waveforms. The effect of additive Gaussian noise on the performance of the four OA removal methods was also investigated. This indicated that the performance of the methods was unaffected by an additive Gaussian noise source, as long as the signal-to-noise ratio remained above 50.

Performance of wavelet packet-division multiplexing in impulsive and Gaussian noise

Wavelet packet-division multiplexing (WPDM) is a high-capacity, flexible, and robust multiple-signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. We derive an expression for the probability of error for a WPDM scheme in the presence of both impulsive and Gaussian noise sources and demonstrate that WPDM can provide greater immunity to impulsive noise than both a time-division multiplexing scheme and an orthogonal frequency-division multiplexing scheme.

THE SIGNAL TRACK SEARCH ALGORITHM

In order to detect gravitational waves from partially modelled/unmodelled sources we will need to have in place a group of robust data analysis algorithms. We discuss here, a particular time-frequency strategy, namely the Signal Track Search (STS) strategy, which is both robust and sensitive for a certain class of signals buried in Gaussian noise. We assume that the signal is a a broadband burst containing several cycles. Our basic strategy involves the construction of time-frequency maps of the detector output and subsequently a search for curvilinear structures in the maps. Though this strategy has been found to work extremely well when the noise is Gaussian, it remains to be seen whether the strategy will be effective when the detector output is further contaminated by non Gaussian noise sources. In this article we will discuss various unresolved issues pertaining to the STS algorithm.

Scalable 2D arrays of noise sources for stochasticretina

The design of scalable 2D arrays of Gaussian white noise sources is addressed. Two original circuits based on cellular automata are described, and the choice of the cellular automaton transition function is discussed.

The pion nucleon sigma term with dynamical Wilson fermions a feasibility study

In a full QCD lattice study with N f = 2 Wilson fermions, we seek to optimize the signals for the disconnected contributions to the Pion Nucleon Sigma term σ N . We demonstrate, in form of a numerical analysis, that — in order to achieve a tolerable signal to noise-ratio in full QCD - it is advantageous to work with a Z 2-noise source rather than to use Gaussian noise sources or to rely only on gange invariance to cancel non-gauge-invariant background. We find that 10 Z 2-noise sources suffice on our sample (about 150 independent QCD configurations at β = 5.6 on 16 3 × 32 with κ sea = 0.157, equivalent to M π M ϱ = 0.7(1) , to achieve decent signals and adequate fluctuations, rather than 300 such sources as recently used in quenched simulations.

Design of Wiener filters using a cumulant based MSE criterion

This paper proposes a cumulant (higher-order statistics) based mean-square-error (MSE) criterion for the design of Wiener filters when both the given wide-sense stationary random signal x( n) and the desired signal d( n) are non-Gaussian and contaminated by Gaussian noise sources. It is theoretically shown that the designed Wiener filter associated with the proposed criterion is identical to the conventional correlation (second-order statistics) based Wiener filter as if both x( n) and d( n) were noise-free measurements. As the latter, the former can also be obtained by solving a cumulant-based Wiener-Hopf equation associated with a (cumulant-based) orthogonality principle. Then a generalized cumulant projection theorem is proposed which includes the projection of cumulants to correlations associated with the proposed cumulant-based MSE criterion and that associated with Delopoulos and Giannakis' cumulant-based MSE criterion as special cases. Moreover, the proposed cumulant-based MSE criterion and Delopoulos and Giannakis' cumulant-based MSE criterion are equivalent for cumulant order M = 3. Some simulation results for system identification and time delay estimation are then provided to demonstrate the good performance of the proposed cumulant-based Wiener filter. Finally, we draw some conclusions.

The performance of bearing estimation using spatial domain forward–backward predictor with higher-order statistics

The modified forward–backward linear predictor (MFBLP) methods with higher-order statistics, viz., the second-order statistics and the fourth-order cumulants, together with the broadband array structure are developed in this paper for bearing estimation. Here, the desired source signals of interest are narrow band and the additive Gaussian noise sources in the related sensors are assumed to be spatially correlated or uncorrelated with each other and white/colored processes in the temporal domain. In this paper, the MFBLP method with second-order statistics for bearing estimation will be emphasized. Moreover, to extract the principal eigenvalues of presented MFBLP methods a new search algorithm is also proposed. An analytical study of the MFBLP method with second-order statistics is first developed, under the assumption that the additive noise is white Gaussian process. From the observation of analytic results, a modification of the MFBLP method with second-order statistics is suggested. From simulation results, it is shown that the MFBLP methods with higher-order statistics is superior to the conventional MFBLP method with the linear array data directly, in terms of threshold signal-to-noise ratio (SNR). This is especially true when data length becomes relatively larger. Moreover, the performance improvement of using the new search algorithm together with all the MFBLP methods is discussed thoroughly.

Kanalkapazität intensitätsmodulierter optischer Übertragungssysteme mit Direktempfängern

The channel capacity (in the sense of information theory) of an intensity-modulated optical transmission system is calculated with realistic boundary conditions. It is shown that a boundary condition for the transmitted signal in which the mean optical power is limited, does not lead to a limitation of the channel capacity. Because of this reason, a new and more realistic boundary condition is derived, in which a linear combination of the mean and the mean squared value of the optical power is limited. For the calculation, the model of the optical transmission system can be reduced to a single-sided hard limiter which prevents the optical power from becoming negative, and an additive coloured Gaussian noise source. For this transmission channel, no general solution for the channel capacity is known in literature. In the present contribution, with the help of simple approximations, upper and lower bounds for the channel capacity are derived. A numerical example shows that these bounds are very close together.

Scalable array of Gaussian white noise sources foranalogue VLSI implementation

A novel method for generating arrays of Gaussian white noise sources is described. Arrays of binary pseudorandom generators are obtained using a cellular automaton, and each binary source is converted into an independent Gaussian noise source. An electronic implementation is described.

An automatic characterization of a Gaussian noise source for undergraduate electronics laboratory

This paper describes a technique which allows the probability density and the probability distribution functions of a Gaussian noise source to be obtained in a very simple, low cost way. First a high-level noise source is described and the characterization of this source is done using only standard parts available at low cost and an easy-to-make test set. Probability density and distribution functions are measured using a synchronous modulation-demodulation technique and recorded by means of a digital storage oscilloscope connected to a compatible PC. This laboratory experiment is used by undergraduate students (of French IUT) with limited knowledge in electronics and mathematics to compare theoretical properties on noise probability with practical measurements. In this laboratory they have to analyze the technique used to measure probability density and distribution functions and to identify the Gaussian noise source in terms of mean value and variance. Finally they have to compare these quantities to those obtained by direct measurements with a "true RMS" voltmeter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Direction of arrival estimation in the presence of distributed noise sources: Cumulant based approach

In the past few years there have been attempts to develop subspace methods for DoA (direction of arrival) estimation using a fourth-order cumulant which is known to de-emphasize Gaussian background noise. To gauge the relative performance of the cumulant MUSIC (MUltiple SIgnal Classification) (c-MUSIC) and the standard MUSIC, based on the covariance function, an extensive numerical study has been carried out, where a narrow-band signal source has been considered and Gaussian noise sources, which produce a spatially correlated background noise, have been distributed. These simulations indicate that, even though the cumulant approach is capable of de-emphasizing the Gaussian noise, both bias and variance of the DoA estimates are higher than those for MUSIC. To achieve comparable results the cumulant approach requires much larger data, three to ten times that for MUSIC, depending upon the number of sources and how close they are. This is attributed to the fact that in the estimation of the cumulant, an average of a product of four random variables is needed to make an evaluation. Therefore, compared to those in the evaluation of the covariance function, there are more cross terms which do not go to zero unless the data length is very large. It is felt that these cross terms contribute to the large bias and variance observed in c-MUSIC. However, the ability to de-emphasize Gaussian noise, white or colored, is of great significance since the standard MUSIC fails when there is colored background noise. Through simulation it is shown that c-MUSIC does yield good results, but only at the cost of more data.

Complex ambiguity functions using nonstationary higher order cumulant estimates

The complex ambiguity function based on second-order statistics (CAF-SOS) has been used to simultaneously estimate the frequency-delay of arrival (FDOA) and time-delay of arrival (TDOA) between two signal measurements; its performance, however, is sensitive to the correlation between two additive noise sources. When the noise sources are assumed to be Gaussian, we develop a new complex ambiguity function based on higher order statistics (CAF-HOS) that reduces the unknown noise-correlation effect. The new CAF-HOS algorithm utilizes nonstationary higher order cross cumulant estimates and their Fourier transform. In fact, we suggest a nonstationary estimate of fourth-order cross-cumulants and obtain the analytical expressions for its mean value and variance. We compare the analytical expressions with results obtained by Monte Carlo runs. Also, we compare the performance of the new complex ambiguity function based on fourth-order statistics (CAF-FOS) against the CAF-SOS algorithm using different Gaussian noise sources, different signals of interest, different signal-to-noise ratios, and different lengths of data.

Crosstalk and channel spacing in a coherent multichannel system using erbium doped fibre amplifiers

The influence of optical amplification with an erbium doped fibre amplifier (FDFA) on coherent multichannel (CMC) transmission is investigated experimentally. The authors found that exactly the same crosstalk/signal ratio can be tolerated in a CMC-system with and without EDFA. They observed no noise floor nor other effects caused by spectral broadening due to the fibre amplifier phase noise. The main influence of the EDFA is (homogeneous) gain saturation. For deep saturation of the EDFA an increase of the noise figure is expected. They conclude that EDFA noise and crosstalk can be considered independent additive (Gaussian) noise sources to the system noise. >

Estimation of frequency-delay of arrival (FDOA) using fourth-order statistics in unknown correlated Gaussian noise sources

A new family of nonparametric and parametric methods based on fourth-order statistics for the estimation of the frequency-delay of arrival (FDOA) between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way, is presented. The new family of FDOA estimation methods utilizes the fourth-order cumulants or 1-D Fourier transforms of sliced fourth-order cumulants of the two signal measurements. It is demonstrated that the new family of FDOA estimation methods suppresses the effect due to correlated Gaussian measurement noises and outperforms existing second-order statistics-based FDOA estimation methods using either cross-ambiguity function or MUSIC algorithm. Various simulation results are presented for different types of signals, different lengths of data, and different signal-to-noise ratios.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>