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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗
NASA NTRS1977

Analysis of a first order phase locked loop in the presence of Gaussian noise

A first-order digital phase locked loop is analyzed by application of a Markov chain model. Steady state loop error probabilities, phase standard deviation, and mean loop transient times are determined for various input signal to noise ratios. Results for direct loop simulation are presented for comparison.

Blasche, P. R.↗
NASA NTRS1989

Simple proof of the concavity of the entropy power with respect to Gaussian noise

A very simple proof of M. H. Costa's result that the entropy power of Xt = X + N (O, tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new inequalities about Fisher information, or at least to exploit the existing ones in new ways.

Dembo, Amir↗
NASA NTRS2002

Estimating the Single-Trial Characteristics of Event-Related Responses: Evaluation of the MCERP Algorithm

Single-trial event-related responses collected during the course of an experiment are typically averaged before analysis resulting in a rather crude picture of event-related brain dynamics. It has been quite clear for some time that these responses exhibit trial-to-trial variability: however, the computational techniques necessary to deal with such responses in noisy conditions have not been available. To this end we have developed the multiple-component, event-related potential model (mcERP), which assumes that the each event-related response consists of a sum of multiple evoked components each described by a stereotypical waveshape. These waveshapes are allowed to vary in amplitude and onset latency from trial to trial, which allows us to capture, to first-order, the trial-dependent variations in event-related brain dynamics. We have constructed many sets of synthetic data designed to simulate intracortical recordings from a 15 channel, linear-array multielectrode implanted acutely in V1 of an awake-behaving macaque undergoing visual stimulation with a red light flash. This synthetic data was used to characterize the performance of the mcERP algorithm. First we quantified the degree to which such trial-to-trial variability aids in the identification of multiple components, and we demonstrate that amplitude variability is a more important factor in component separation than latency variability. Second, we quantified the behavior of the algorithm under two distinct signal-to-noise ratio (SNR) conditions: Gaussian noise independently present in each channel, and highly correlated (1/f distributed), far-field noise presented identically in each channel of the array. The mcERP algorithm was found to be robust to noise accurately identifying all component waveshapes and their associated single-trial characteristics down to SNR levels of -20dB for Gaussian noise and -7dB for 1/f far-field noise. Comparisons of the performance of this algorithm with factor analysis (FA) and independent component analysis (ICA) will be described by Knuth et al. (SFN abstracts, 2002). In addition, the advantages of application of mcERP to real data will be described by Shah et al, (these abstracts, 2002: SFN abstracts, 2002).

Knuth, K. H.↗
NASA NTRS2021

Deriving Deformable Mirror Performance Requirements in Simulation with Experimental Verification

Coronagraph instruments rely on predictable and stable deformable mirror (DM) surface displacement to achieve the contrast required to detect Earth-sized exoplanets orbiting nearby Solar-type stars. Anomalous DM behavior, such as unstable or pinned actuators, can limit contrast in coronagraphs. Simulating how these undesired behaviors affect the performance of a high contrast imaging architecture is important for developing requirements on their associated hardware. Simulating a vortex coronagraph (VC) with two deformable mirrors, this study quantifies how the number of pinned actuators affect the performance of Focal Plane Wavefront Sensing and Control algorithms using both Grid Search Electric Field Conjugation (EFC) and Planned EFC, which uses Beta-Bumping. The simulation also quantifies how various types of voltage noise such as zero-mean Gaussian noise, zero-mean periodic noise, and drift can affect the contrast of a VC during an observation run. A tolerance of a change in the Mean Normalized Intensity of ${1\times10^{-11}}$ is allocated to both types of error. If Planned EFC is used, only 1 pinned actuator on both DMs can be tolerated. If only pure Grid Search EFC is used the DMs cannot have any pinned actuators. For the case of zero-mean Gaussian noise and zero-mean periodic noise, one can tolerate a noise standard deviation of no more than ${\sigma = 0.45 \text{ mV}}$. For drift, we can only tolerate ${\sigma = 0.30 \text{ mV}}$ or less. These results show that the DM electronics and the DM themselves need to be nearly defect free to avoid having more than 1 pinned actuator. The electronics need to be tested for different types of noise statistics and that both the average and standard deviation of the noise should be measured.

Dean L. Palmer↗
NASA NTRS1992

Figure of merit for direct-detection optical channels

The capacity and sensitivity of a direct-detection optical channel are calculated and compared to those of a white Gaussian noise channel. Unlike Gaussian channels in which the receiver performance can be characterized using the noise temperature, the performance of the direct-detection channel depends on both signal and background noise, as well as the ratio of peak to average signal power. Because of the signal-power dependence of the optical channel, actual performance of the channel can be evaluated only by considering both transmit and receive ends of the systems. Given the background noise power and the modulation bandwidth, however, the theoretically optimum receiver sensitivity can be calculated. This optimum receiver sensitivity can be used to define the equivalent receiver noise temperature and calculate the corresponding G/T product. It should be pointed out, however, that the receiver sensitivity is a function of signal power, and care must be taken to avoid deriving erroneous projections of the direct-detection channel performance.

Chen, C.-C.↗
NASA NTRS1991

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗
NASA NTRS2010

Separating Gravitational Wave Signals from Instrument Artifacts

Central to the gravitational wave detection problem is the challenge of separating features in the data produced by astrophysical sources from features produced by the detector. Matched filtering provides an optimal solution for Gaussian noise, but in practice, transient noise excursions or "glitches" complicate the analysis. Detector diagnostics and coincidence tests can be used to veto many glitches which may otherwise be misinterpreted as gravitational wave signals. The glitches that remain can lead to long tails in the matched filter search statistics and drive up the detection threshold. Here we describe a Bayesian approach that incorporates a more realistic model for the instrument noise allowing for fluctuating noise levels that vary independently across frequency bands, and deterministic "glitch fitting" using wavelets as "glitch templates", the number of which is determined by a trans-dimensional Markov chain Monte Carlo algorithm. We demonstrate the method's effectiveness on simulated data containing low amplitude gravitational wave signals from inspiraling binary black hole systems, and simulated non-stationary and non-Gaussian noise comprised of a Gaussian component with the standard LIGO/Virgo spectrum, and injected glitches of various amplitude, prevalence, and variety. Glitch fitting allows us to detect significantly weaker signals than standard techniques.

Littenberg, Tyson B.↗
NASA NTRS1994

Microwave background fluctuations due to the Sunyaev-Zel'dovich effects in pancakes

We calculate distortions in the microwave background radiation from the Sunyaev-Zel'dovich effect, produced by hot gas in large (approximately 100 Mpc) pancakes. The large-scale distribution of the pancakes is taken to be that of a Voronoi foam. Fluctuations for this scenario are estimated to be on the order of delta T/T is approximately 10(exp -5). Using computer simulations, we produce several 32 deg x 32 deg images with 0.25 deg resolution. These images show characteristic linear features produced when a pancake is viewed nearly edge-on. By calculating the two-point and the degenerate three-point correlation functions, we are able to statistically detect such non-Gaussian features even in the presence of a relatively large amount of Gaussian noise. The degenerate three-point correlation function is found to be particularly useful since it is insensitive to correlated Gaussian noise. We also smooth our data over a 7 deg Full Width at Half Maximum (FWHM) Gaussian window to simulate the Cosmic Background Explorer Satellite (COBE) observations. We find that under such low-resolution conditions, the features are highly suppressed.

Subbarao, M. U.↗
NASA NTRS2014

Application of Machine Learning Algorithms to the Study of Noise Artifacts in Gravitational-Wave Data

The sensitivity of searches for astrophysical transients in data from the Laser Interferometer Gravitationalwave Observatory (LIGO) is generally limited by the presence of transient, non-Gaussian noise artifacts, which occur at a high-enough rate such that accidental coincidence across multiple detectors is non-negligible. Furthermore, non-Gaussian noise artifacts typically dominate over the background contributed from stationary noise. These "glitches" can easily be confused for transient gravitational-wave signals, and their robust identification and removal will help any search for astrophysical gravitational-waves. We apply Machine Learning Algorithms (MLAs) to the problem, using data from auxiliary channels within the LIGO detectors that monitor degrees of freedom unaffected by astrophysical signals. Terrestrial noise sources may manifest characteristic disturbances in these auxiliary channels, inducing non-trivial correlations with glitches in the gravitational-wave data. The number of auxiliary-channel parameters describing these disturbances may also be extremely large; high dimensionality is an area where MLAs are particularly well-suited. We demonstrate the feasibility and applicability of three very different MLAs: Artificial Neural Networks, Support Vector Machines, and Random Forests. These classifiers identify and remove a substantial fraction of the glitches present in two very different data sets: four weeks of LIGO's fourth science run and one week of LIGO's sixth science run. We observe that all three algorithms agree on which events are glitches to within 10% for the sixth science run data, and support this by showing that the different optimization criteria used by each classifier generate the same decision surface, based on a likelihood-ratio statistic. Furthermore, we find that all classifiers obtain similar limiting performance, suggesting that most of the useful information currently contained in the auxiliary channel parameters we extract is already being used. Future performance gains are thus likely to involve additional sources of information, rather than improvements in the MLAs themselves.

gravitational-wave data↗
DOE OSTI2026

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗