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NASA NTRS1987

Sampling theory applied to measurement and analysis of temperature for climate studies

Of all the errors discussed in climatology literature, aliasing errors caused by undersampling of unsmoothed or improperly smoothed temperature data seem to be completely overlooked. This is a serious oversight in view of long-term trends of 1 K or less. Adequate sampling of properly smoothed data is demonstrated with a Hamming digital filter. It is also demonstrated that hourly temperatures, daily averages, and annual averages free of aliasing errors can be obtained by use of a microprocessor added to standard weather sensors and recorders.

Edwards, Howard B.↗

NASA NTRS1991

On the rotation and skew-symmetric forms for incompressible flow simulations

A variety of numerical simulations of transition and turbulence in incompressible flow are presented to compare the commonly used rotation form with the skew-symmetric (and other) forms of the nonlinear terms. The results indicate that the rotation form is much less accurate than the other forms for spectral algorithms which include aliasing errors. For de-aliased methods the difference is minimal.

Zang, Thomas A.↗

NASA NTRS1991

An information theory of image gathering

Shannon's mathematical theory of communication is extended to image gathering. Expressions are obtained for the total information that is received with a single image-gathering channel and with parallel channels. It is concluded that the aliased signal components carry information even though these components interfere with the within-passband components in conventional image gathering and restoration, thereby degrading the fidelity and visual quality of the restored image. An examination of the expression for minimum mean-square-error, or Wiener-matrix, restoration from parallel image-gathering channels reveals a method for unscrambling the within-passband and aliased signal components to restore spatial frequencies beyond the sampling passband out to the spatial frequency response cutoff of the optical aperture.

Fales, Carl L.↗

NASA NTRS1993

Multiresponse Imaging For Improved Resolution

Images restored with resolution finer than sampling lattice. Multiresponse imaging overcomes sampling-passband constraint and critically constrained only by optical response and sensitivity of image-gathering device. Process consists of multiresponse image gathering and Wiener-matrix restoration. Image-gathering process acquires sequence of images, each with different optical response so within-pass-band and aliased signal components weighted differently. Wiener-matrix filter, in turn, unscrambles within-passband and aliased frequency components of undersampled signal and restores them up to cutoff frequency of optical response.

Fales, Carl L., Jr.↗

NASA NTRS1993

Characteristics of vertical and lateral tunnel turbulence measured in air in the Langley Transonic Dynamics Tunnel

Preliminary measurements of the vertical and lateral velocity components of tunnel turbulence were obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the test medium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmospheric pressure. Standard deviations of turbulence velocities were determined and power spectra were computed. Unconstrained optimization was employed to determine parameter values of a general spectral model of a form similar to that used to describe atmospheric turbulence. These parameters, and others (notably break frequency and integral scale length), were determined at each test condition and compared with those of Dryden and Von Karman atmospheric turbulence spectra. When the data were discovered to be aliased, the spectral model was modified to account for and 'eliminate' the aliasing.

Sleeper, Robert K.↗

NASA NTRS1994

The Martian atmospheric planetary boundary layer stability, fluxes, spectra, and similarity

This is the first analysis of the high frequency data from the Viking lander and spectra of wind, in the Martian atmospheric surface layer, along with the diurnal variation of the height of the mixed surface layer, are calculated for the first time for Mars. Heat and momentum fluxes, stability, and z(sub O) are estimated for early spring, from a surface temperature model and from Viking Lander 2 temperatures and winds at 44 deg N, using Monin-Obukhov similarity theory. The afternoon maximum height of the mixed layer for these seasons and conditions is estimated to lie between 3.6 and 9.2 km. Estimations of this height is of primary importance to all models of the boundary layer and Martian General Circulation Models (GCM's). Model spectra for two measuring heights and three surface roughnesses are calculated using the depth of the mixed layer, and the surface layer parameters and flow distortion by the lander is also taken into account. These experiments indicate that z(sub O), probably lies between 1.0 and 3.0 cm, and most likely is closer to 1.0 cm. The spectra are adjusted to simulate aliasing and high frequency rolloff, the latter caused both by the sensor response and the large Kolmogorov length on Mars. Since the spectral models depend on the surface parameters, including the estimated surface temperature, their agreement with the calculated spectra indicates that the surface layer estimates are self consistent. This agreement is especially noteworthy in that the inertial subrange is virtually absent in the Martian atmosphere at this height, due to the large Kolmogorov length scale. These analyses extend the range of applicability of terrestrial results and demonstrate that it is possible to estimate the effects of severe aliasing of wind measurements, to produce a models which agree well with the measured spectra. The results show that similarity theory developed for Earth applies to Mars, and that the spectral models are universal.

Tillman, James E.↗

NASA NTRS1994

The boundary layer of Mars: Fluxes, stability, turbulent spectra, and growth of the mixed layer

Spectra of wind from high-frequency measurements in the Martian atmospheric surface layer, along with the diurnal variation of the height of the mixed surface layer, are calculated for the first time for Mars. Heat and momentum fluxes, stability, and z(sub 0) are estimated for early spring from a surface temperature model and from Viking Lander 2 temperatures and winds at 44 deg N, using Monin-Obukhov similarity theory. Flow distortion by the lander is also taken into account. Model spectra for two measuring heights and three surface roughnesses are calculated using the depth of the mixed layer and the surface-layer parameters. These experiments indicate that z(sub 0) probably lies between 1.0 and 3.0 cm, and most likely is closer to 1.0 cm. The spectra are adjusted to simulate aliasing and high-frequency rolloff, the latter caused by both the sensor response and the large Kolmogorov length on Mars. Since the spectral models depend on the surface parameters, including the estimated surface temperature, their agreement with the calculated spectra indicates that the surface-layer estimates are self-consistent. This agreement is especially noteworthy in that the inertial subrange is virtually absent in the Martian atmosphere at this height, due to the large Kolmogorov length scale. These analyses extend the range of applicability of terrestrial results and demonstrate that it is possible to estimate the effects of severe aliasing of wind measurements, to produce models that agree well with the measured spectra. The results show that similarity theory developed for Earth applies to Mars, and that the spectral models are universal.

Tillman, James E.↗

NASA NTRS1994

Response of a two-dimensional dual-Doppler radar wind synthesis

The wind field resulting from a two-dimensional dual-Doppler synthesis algorithms is spectrally modified from the true wind field. The effects of spatial filtering on wind fields from the processes of interpolation, the averaging of pulses, and the effect of the finite radar pulse dimension were assessed. The effect resulting from the use of different interpolation techniques was also evaluated. Of those techniques tested, the best are the Cressman distance-weighted averaging and linear distance-weighted averaging, with the closest neighbor and uniform weighting having more undesirable characteristics. The optimum influence radius is defined as the influence radius at which the ratio of the rms difference between the Fourier and least-squares responses (a measure of the aliasing) and the variance of the filtered wind field is minimized. This seeks to minimize the effect of energy aliased into scales other than the input wavelength. For the Cressman interpolation technique, the optimum influence radius is between 1.85 and 2.25 times the maximum data spacing. The range of acceptable influence radii includes consideration of the filtering by the radar of the data as it is collected, as well as the resolution of the final dataset. The optimum influence radius is dependent upon the largest data separation in the analysis domain. The absolute optimum influence radius is not significantly affected by inclusion of the radar-beam filtering effects.

Given, Terence↗

NASA NTRS1999

Fidelity Analysis of Sampled Imaging Systems

Many modeling, simulation and performance analysis studies of sampled imaging systems are inherently incomplete because they are conditioned on a discrete-input, discrete-output model that only accounts for blurring during image acquisition and additive noise. For those sampled imaging systems where the effects of digital image acquisition, digital filtering and reconstruction are significant, the modeling, simulation and performance analysis should be based on a more comprehensive continuous-input, discrete-processing, continuous-output end-to-end model. This more comprehensive model should properly account for the low-pass filtering effects of image acquisition prior to sampling, the potentially important noiselike effects of the aliasing caused by sampling, additive noise due to device electronics and quantization, the generally high-boost filtering effects of digital processing, and the low-pass filtering effects of image reconstruction. This model should not, however, be so complex as to preclude significant mathematical analysis, particularly the mean-square (fidelity) type of analysis so common in linear system theory. We demonstrate that, although the mathematics of such a model is more complex, the increase in complexity is not so great as to prevent a complete fidelity-metric analysis at both the component level and at the end-to-end system level: that is, computable mean-square-based fidelity metrics are developed by which both component-level and system-level performance can be quantified. In addition, we demonstrate that system performance can be assessed qualitatively by visualizing the output image as the sum of three component images, each of which relates to a corresponding fidelity metric. The cascaded, or filtered, component accounts for the end-to-end system filtering of image acquisition, digital processing, and image reconstruction; the random noise component accounts for additive random noise, modulated by digital processing and image reconstruction filtering; and the aliased noise component accounts for the frequency folding effect of sampling, modulated by digital processing and image reconstruction filtering.

Park, Stephen K.↗

NASA NTRS2005

Effects of High-frequency Wind Sampling on Simulated Mixed Layer Depth and Upper Ocean Temperature

Effects of high-frequency wind sampling on a near-global ocean model are studied by forcing the model with a 12 hourly averaged wind product and its 24 hourly subsamples in separate experiments. The differences in mixed layer depth and sea surface temperature resulting from these experiments are examined, and the underlying physical processes are investigated. The 24 hourly subsampling not only reduces the high-frequency variability of the wind but also affects the annual mean wind because of aliasing. While the former effect largely impacts mid- to high-latitude oceans, the latter primarily affects tropical and coastal oceans. At mid- to high-latitude regions the subsampled wind results in a shallower mixed layer and higher sea surface temperature because of reduced vertical mixing associated with weaker high-frequency wind. In tropical and coastal regions, however, the change in upper ocean structure due to the wind subsampling is primarily caused by the difference in advection resulting from aliased annual mean wind, which varies with the subsampling time. The results of the study indicate a need for more frequent sampling of satellite wind measurement and have implications for data assimilation in terms of identifying the nature of model errors.

mixed layered depth↗

NASA NTRS2004

Low-Cutoff, High-Pass Digital Filtering of Neural Signals

The figure depicts the major functional blocks of a system, now undergoing development, for conditioning neural signals acquired by electrodes implanted in a brain. The overall functions to be performed by this system can be summarized as preamplification, multiplexing, digitization, and high-pass filtering. Other systems under development for recording neural signals typically contain resistor-capacitor analog low-pass filters characterized by cutoff frequencies in the vicinity of 100 Hz. In the application for which this system is being developed, there is a requirement for a cutoff frequency of 5 Hz. Because the resistors needed to obtain such a low cutoff frequency would be impractically large, it was decided to perform low-pass filtering by use of digital rather than analog circuitry. In addition, it was decided to timemultiplex the digitized signals from the multiple input channels into a single stream of data in a single output channel. The signal in each input channel is first processed by a preamplifier having a voltage gain of approximately 50. Embedded in each preamplifier is a low-pass anti-aliasing filter having a cutoff frequency of approximately 10 kHz. The anti-aliasing filters make it possible to couple the outputs of the preamplifiers to the input ports of a multiplexer. The output of the multiplexer is a single stream of time-multiplexed samples of analog signals. This stream is processed by a main differential amplifier, the output of which is sent to an analog-to-digital converter (ADC). The output of the ADC is sent to a digital signal processor (DSP).

Mojarradi,Mohammad↗

NASA NTRS2020

Search and Rescue under the Forest Canopy using Multiple UAS

We consider the problem of multi-robot search and rescue under the forest canopy. Forest is a particularly challenging environment for collaborative mapping and exploration, mainly due to the existence of severe perceptual aliasing, which hinders reliable mutual localization and map fusion. Our proposed system features unmanned aerial vehicles (UAVs) with onboard sensing and autonomy. Each UAV runs a lightweight filtering algorithm for local state estimation, and a dynamic-aware frontier selection algorithm for fast exploration. The essential and computationally intensive task of collaborative simultaneous localization and mapping (CSLAM) is performed at a central ground station. To handle perceptual aliasing, we make use of stable landmarks extracted from trees, which significantly improve precision and recall during place recognition. Furthermore, to recover from incorrect pairwise data associations during loop closure, we propose a novel procedure for global data association based on recently developed techniques on cycle consistent multiway matching. Our algorithm returns a global data association that is guaranteed to be cycle consistent, and is shown to significantly improve precision compared to the input pairwise associations. The overall multi-UAV system is extensively validated during real-world collaborative exploration missions in a forest at NASA Langley Research Center.

Multi-robot systems↗

NASA NTRS2022

Estimating the Migrating Diurnal Tide Component of Mesospheric Water Vapor

This work presents a method for estimating the migrating diurnal tide (DW1) component of mesospheric H2O from observations of the temperature tide and zonal-mean H2O made by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument. This work first shows that a 2D least-squares fit on SABER H2O yields an erroneous DW1 due to retrieval algorithm problems. Consequently, the adiabatic displacement method is used. Applying the method to SABER observations and comparing it with Microwave Limb Sounder (MLS) H2O observations reveals that the method reproduces the MLS-observed H2O DW1 component best in March and June over low-latitudes in the altitude range between 65 and 75 km where errors range between +5% and +20%. Applying the method for simulations using the Specified Dynamics—Whole Atmosphere Community Climate Model with Ionosphere/Thermosphere eXtension (SD-WACCM-X) indicates that in the model, it is best only in March and not in June. Model simulations further showed that in March, theoretical errors due to the vertical advection assumption and aliasing are best at less than +13% for the low-latitudes and altitudes between 65 and 75 km. These results, therefore, lead to the conclusion that despite the errors in the vertical advection assumption and aliasing, the adiabatic displacement method performs best in estimating mesospheric H2O DW1 with SABER observations during both March equinox and June solstice over the low latitudes between 65 and 75 km. Results also show that SD-WACCM-X satisfactorily simulates the H2O DW1 magnitude and mechanisms only in the March equinox period.

h20↗

NASA NTRS2025

Source-Time Dominant Modeling of the Doppler Shift for the Auralization of Moving Sources

When developing an auralization for acoustic scenarios involving moving sources and receivers, one key feature is the ability to simulate the Doppler shift, i.e., the changing frequency content from the receiver’s perspective. As the time-varying delay between a source and receiver is what accounts for the Doppler shift, an approximation of this delay is required to successfully render the changes in frequency content at the receiver. Depending on the signal-processing strategy chosen to accomplish this task, there is, how-ever, a potential to introduce audible artifacts due to frequency folding (aliasing), frequency replication (imaging), and broadband noise. In this paper we dis-cuss the manifestation of such artifacts and propose a method to eliminate them, which can be integrated into the digital signal processing chain of larger auralization schemes. The method is built upon a source-time dominant approach and uses a combination of oversampling, interpolation, and time-varying filtering to predict and eliminate frequency regions at the receiver that are vulnerable to aliasing and imaging. We demonstrate the strengths and weaknesses of the method using a circularly moving source with a fixed receiver.

Auralization↗

DOE OSTI2024

Conservative discontinuous Galerkin interpolation: Sheared boundary conditions

Local studies of accretion disks and laboratory magnetized plasmas employ analytical coordinate mappings that introduce sheared boundary conditions (BCs). Here, we present a discontinuous Galerkin (DG) algorithm to apply such BCs based on projections and quadrature-free integration. The procedure is high-order accurate, preserves moments exactly and works in multiple dimensions. Tests of increasing complexity are provided, beginning with translations of one and two dimensional fields, followed by 3D and 5D simulations with sheared (twist-shift) BCs. Results show that the algorithm is (p + 1)-order accurate in the DG representation and (p + 2) -order accurate in the cell averages, with p being the order of the polynomial basis. Quantification of the algorithm's hyperdiffusion and discussion of aliasing errors are given. This technique enables conservative local simulations of plasma turbulence with DG, not possible until now.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Impacts of swinging door lossy compression of synchrophasor data

As the number of operational Phasor Measurement Units (PMUs) is increasing, compression is becoming crucial for efficiently transferring and storing enormous amount of synchrophasor data continuously measured from a power system. Some utilities in the U.S. have already adopted a nonlinear compression technique, called Swinging Door Algorithm (SDA), assuming compressed data meets technical and regulatory requirements without resulting in any degradation of the measurements. This paper studies impacts of this compression algorithm on field measured and simulated PMU data, and presents results from spectral analyses of raw and decompressed measurements. The results show blind application of the SDA compression alters frequency content in the measurements and introduces false harmonics and aliasing. These can lead to false conclusions being drawn from the measurements about the power system condition.

42 ENGINEERING↗

DOE OSTI2020

Improved C 1 shape functions for simplex meshes

Using continuously-differentiable (C 1 ) interpolation methods previously developed for computer visualization and other applications, a new class of shape functions is constructed and applied to electrostatic (ES) Particle-In-Cell (PIC) simulations on simplex (triangle or tetrahedral) meshes. The resulting shape functions are non-negative and partition unity,and lead to a reduction of shot noise and aliasing associated with particle interpolation to and from the mesh. For an energy-conserving implementation as chosen, C 1 interpolation of the potential leads to a continuous (C 0 ) electric field, with associated improved fidelity of particle motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗