A constructive derivation of the capacity of a bandlimited channel
Constructive derivation of capacity of bandwidth limited channel in presence of additive Gaussian white noise
GAUSSIAN NOISE↗
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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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Adaptive filtering Interim report
Adaptive filter with inaccuracies approximated by Gaussian white noise input and determination of covariance for most probable residual sequence
GAUSSIAN NOISE↗
Orthogonal tree codes for communication in the presence of white Gaussian noise.
Convolutional encoder for orthogonal tree codes in presence of white Gaussian noise
ENCODER↗
On signal design by the R/0/ criterion for non-white Gaussian noise channels
The use of the cut-off rate criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate for vector channels with additive non-white Gaussian noise and unquantized demodulation is derived. When the signal input to the channel is a continuous random vector, maximization of the cut-off rate with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize the cut-off rate with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. As an example, the rectangular signal set which has the water-filling average energy distribution and the optimum rectangular set are compared.
Bordelon, D. L.↗
X-ray variability of Cygnus X-1 in its soft state
Observations from the Rossi X-ray Timing Explorer (RXTE) of Cyg X-1 in the soft state and during the soft to hard transition are examined. The results of this analysis confirm previous conclusions that for this source there is a settling period (following the transition from the hard to soft state during which the low energy spectrum varies significantly, while the high energy portion changes little) during which the source reaches nominal soft state brightness. This behavior can be characterized by a soft low energy spectrum and significant low frequency 1/f noise and white noise on the power density spectrum, which becomes softer upon reaching the true soft state. The low frequency 1/f noise is not observed when Cyg X-1 is in the hard state, and therefore appears to be positively correlated with the disk mass accretion rate. The difference in the observed spectral and timing properties between the hard and soft states is qualitatively consistent with a fluctuating corona model.
Cui, W.↗
Optimal inputs for parameter estimation in dynamic systems with white observation noise.
Optimal deterministic inputs derived for estimating dynamic control system parameters from white observation noise
Nahi, N. E.↗
Cosmic Infrared Background Fluctuations and Zodiacal Light
We performed a specific observational test to measure the effect that the zodiacal light can have on measurements of the spatial fluctuations of the near-IR (near-infrared)background. Previous estimates of possible fluctuations caused by zodiacal light have often been extrapolated from observations of the thermal emission at longer wavelengths and low angular resolution or from IRAC (Infrared Array Camera) observations of high-latitude fields where zodiacal light is faint and not strongly varying with time. The new observations analyzed here target the COSMOS (Cosmic Evolution Survey) field at low ecliptic latitude where the zodiacal light intensity varies by factors of approximately 2 over the range of solar elongations at which the field can be observed. We find that the white-noise component of the spatial power spectrum of the background is correlated with the modeled zodiacal light intensity. Roughly half of the measured white noise is correlated with the zodiacal light, but a more detailed interpretation of the white noise is hampered by systematic uncertainties that are evident in the zodiacal light model. At large angular scales (greater than or approximately equal to 100 arcseconds) where excess power above the white noise is observed, we find no correlation of the power with the modeled intensity of the zodiacal light. This test clearly indicates that the large-scale power in the infrared background is not being caused by the zodiacal light.
cosmology: observations aEuro" diffuse radiation a↗
Choosing channel quantization levels and viterbi decoding for space diversity reception over the additive white Guassian noise channel
Previous work in the area of choosing channel quantization levels for a additive white Gaussian noise channel composed of one receiver-demodulator is reviewed, and how this applies to the Deep Space Network composed of several receiver-demodulators (space diversity reception) is shown. Viterbi decoding for the resulting quantized channel is discussed.
Kalson, S.↗
On signal design by the R sub 0 criterion for non-white Gaussian noise channels
The use of the R sub 0 criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate R sub 0 for vector channels with additive nonwhite Gaussian noise and unquantized demodulation is derived. When the signal unput to the channel is a continuous random vector, maximization of R sub 0 with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize R sub 0 with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. A necessary condition on a constrained energy, finite signal set is found which maximizes a Taylor series approximation of R sub 0. This signal set is compared with the finite signal set which has the water-filling average energy distribution.
Bordelon, D. L.↗
Analysis of first and second order binary quantized digital phase-locked loops for ideal and white Gaussian noise inputs
Specific configurations of first and second order all digital phase locked loops are analyzed for both ideal and additive white gaussian noise inputs. In addition, a design for a hardware digital phase locked loop capable of either first or second order operation is presented along with appropriate experimental data obtained from testing of the hardware loop. All parameters chosen for the analysis and the design of the digital phase locked loop are consistent with an application to an Omega navigation receiver although neither the analysis nor the design are limited to this application.
Blasche, P. R.↗
Red Noise–based False Alarm Thresholds for Astrophysical Periodograms via Whittle’s Approximation to the Likelihood
Astronomers who search for periodic signals using Lomb–Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical time series suffer from red noise. Prewhitening is a statistical technique in which a continuum model is subtracted from the log power spectrum estimate, after which the observer can proceed with a white-noise treatment. Here we present a prewhitening-based method of calculating frequency-dependent FALs. We fit power laws and autoregressive models of order 1 to each Lomb–Scargle periodogram by minimizing the Whittle approximation to the negative log-likelihood (NLL), then calculate FALs based on the best-fit model power spectrum. Our technique is a novel extension of the Whittle NLL to datasets with uneven time sampling. We demonstrate FAL calculations using observations of α Cen B, GJ 581, HD 192310, synthetic data from the radial velocity (RV) fitting challenge, and Kepler observations of a differential rotator. The Kepler data analysis shows that only true rotation signals are detected by red noise FALs, while white noise FALs suggest all spurious peaks in the low-frequency range are significant. A high-frequency sinusoid injected into α Cen B logR$'$ HK observations exceeds the 1% red noise FAL despite having only 8.9% of the power of the dominant rotation signal. In a periodogram of HD 192310 RVs, peaks associated with differential rotation and planets are detected against the 5% red noise FAL without iterative model fitting or subtraction. The software for calculating red noise–based FALs is available on GitHub.
Astrostatistics (1882)↗
An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise
An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.
Reddy, C. P.↗
Improved Measurement of Coherence in Presence of Instrument Noise
A method for correcting measured coherence spectra for the effect of incoherent instrument noise has been developed and demonstrated. Coherence measurements are widely used in engineering and science to determine the extent to which two signals are alike. The signals may come from two different sources or from the same source at different times. The coherence of time-lagged signals from a single source is an excellent indication of the effective lifetime of the signal components as a function of their frequency. Unfortunately, incoherent instrument noise will bias the measurement to lower values and may lead the user of the data to false conclusions about the longevity of significant features. The new method may be used whenever both the signal and noise power spectra are known and the noise is incoherent both with the signal and with itself at the applicable time delays. It provides a corrected coherence spectrum given the measured coherence and power spectra. For powerlaw signal spectra and instrumental white noise, the correction formula takes a particularly simple and explicit form. Since many geophysical signals exhibit powerlaw behavior and most instrument noise spectra approach white noise, the simplified form should be widely applicable in meteorology, oceanography, geology, and planetary geophysics.
Merceret, Francis J.↗
The Effect of Information Feedback Upon Psychophysical Judgments
An analysis was made of the role of presentation schedules and information feedback on performance in a forced-choice signal detection task. The experimental results indicate that information feedback facilitates performance, but only for certain presentation schedules. The present study was designed to assess performance in a signal detection task under two conditions of information feedback. In the I-condition, S was told on each trial whether his detection response was correct or incorrect; in the !-condition S was given no feedback regarding the correctness of his response. The task involved a 2-response, forced-choice auditory detection problem. On each trial 2 temporal intervals were defined and S was required to report which interval he believed contained the signal; i. e., in one interval a tone burst in a background of white noise was presented, while the other interval contained only white noise. A trial will be denoted as s1 or s2, depending on whether the signal was embedded in the 1st or 2nd interval; the S's response will be denoted A1 or A2 to indicate which interval he reported contained the signal. The probability of an s1 trial will be denoted as y. In this study two values of y were used (.50 and.75) and, as indicated above, two conditions of information feedback. Thus there were 4 experimental conditions (501, · 50I, 751, 75I); each S was run under all 4 conditions. Method Gaussian noise was presented binaurally in S's headphones throughout a test session and the signal was a 1000-cps sinusoid tone; the tone was presented for 100 msec. including equal fall and rise times of 20 msec. The ratio of signal energy to noise power in a unit bandwidth was 2.9, and was constant throughout the study. The. S was seated before a stimulus display board. On each trial a red warning light was flashed for 100 msec. Two amber lights then came on successively each for 1 sec.; these lights defined the 2 observation intervals. The onset of the signal occurred 500 msec. after the onset of one of the observation intervals. After the second amber light went off, S indicated his response by pressing 1 of 2 wand switches under cards reading "1st interval" and "2nd interval." For the !-condition a green light flashed on above the correct response key after S's response; the green light was omitted in the !-condition. Each trial lasted 6 sec. The S's were 12 male college students with normal hearing. They were run for two practice sessions followed by 20 test sessions. Test sessions were run on consecutive days, 350 trials/day. Each day S ran on 1 of the 4 experimental conditions; in successive 4-day blocks S ran one day on each of the 4 experimental conditions in a random order. Thus, over 20 days each of the experimental conditions was repeated 5 times.
Atkinson, Richard C.↗
Geosat Follow-On (GFO) Altimeter Document Series: GFO On-Orbit Altimeter Noise Assessment - Volume 2
The purpose of this report is to present the results of an analysis of the white noise in Geosat Follow-On (GFO) altimeter data. The Repeat-Track Method was used to determine noise level. This approach was developed at TASC and has been used to quantify noise levels of all previous satellite altimeter missions. The GFO altimeter was designed to have an RMS white noise level of less than 3.5 centimeters for significant wave height less than 2 meters. The results of the analysis presented here show that the GFO altimeter meets this specification.
Driscoll, Mavis L.↗
Detecting and disentangling nonlinear structure from solar flux time series
Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.
Ashrafi, S.↗
Detection in fixed and random noise in foveal and parafoveal vision explained by template learning
Foveal and parafoveal contrast detection thresholds for Gabor and checkerboard targets were measured in white noise by means of a two-interval forced-choice paradigm. Two white-noise conditions were used: fixed and twin. In the fixed noise condition a single noise sample was presented in both intervals of all the trials. In the twin noise condition the same noise sample was used in the two intervals of a trial, but a new sample was generated for each trial. Fixed noise conditions usually resulted in lower thresholds than twin noise. Template learning models are presented that attribute this advantage of fixed over twin noise either to fixed memory templates' reducing uncertainty by incorporation of the noise or to the introduction, by the learning process itself, of more variability in the twin noise condition. Quantitative predictions of the template learning process show that it contributes to the accelerating nonlinear increase in performance with signal amplitude at low signal-to-noise ratios.
NASA Center ARC↗
Temporal averaging of phase measurements in the presence of spurious phase drift - Application to phase-stepped real-time holographic interferometry
A technique that compensates for low spatial frequency spurious phase changes during an interference experiment is developed; it permits temporal averaging of multiple-phase measurements, made before and after object displacement. The method is tested with phase-stepped real-time holographic interferometry applied to cantilever bending of a piezoelectric bimorph ceramic. Results indicate that temporal averaging of the corrected data significantly reduces the white noise in a phase measurement without incurring systematic errors or sacrificing spatial resolution. White noise is reduced from 3 deg to less than 1 deg using these methods.
Ovryn, B.↗