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NASA NTRS1986

Global collocation methods for approximation and the solution of partial differential equations

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.↗

NASA NTRS1986

Rotational modulation in IUE spectra of cool dwarf chromospheres: Data analysis and period search techniques

The IUE spectra of bright F-K dwarfs were used to investigate rotational modulation in chromospheric and transition region emission lines, with Stellingwerf's phase dispersion minimization (PDM) technique as the basis of time series analysis. Sampling-related aliases are found to dominate the PDM spectra in these sparsely sampled, irregularly spaced time series. The star chosen to illustrate the techniques is epsilon Eridani, a young, chromospherically active K2 dwarf. Strong indications of a rotation period close to 2.8 days in epsilon Eridani from 2 seasons of observations, with evidence for the persistence in longitude of the active area(s) over several hundred rotation cycles are found.

Altner, B.↗

NASA NTRS1986

Soft X-ray oscillations during the flare of 7 August 1972

Unique observations from OSO-7 of the intense flare on 7 August 1972 are presented, showing 1.6 second oscillations in it's soft X-ray emission which are long enduring, extremely regular, and initially of large amplitude. For approximately 20 minutes just after flare maximum, the X-ray intensity of an area 20 arc second square near the flare's core was monitored with 160 millisecond time resolution in two channels, 2-8A and 8-16A. Each channel recorded over 700 cycles of the X-ray oscillations, which remained remarkably stable in phase and period throughout the entire observations, but with gradually diminishing amplitude. The observed period does not correspond to any known operational periodicity in either the instrument or the spacecraft and cannot be attributed to aliasing with any other oscillatory component. Channel ratios indicate that both the temperature and electron density of the emitting plasma are enhanced at the peak of each cycle. There is indirect evidence that the X-ray pulsations are occurring only in a relatively small portion of an elongated feature, presumed to be a loop or arcade of loops.

Thomas, Roger J.↗

NASA NTRS1987

Error analysis for spectral approximation of the Korteweg-De Vries equation

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Maday, Y.↗

NASA NTRS1987

Detection of signals by the digital integrate-and-dump filter with offset sampling

The Integrate and Dump Filter (IDF) is used as a matched filter for the detection of signals in additive white Gaussian noise. The performance of the digital integrate and dump filter is evaluated. The case considered is when symbol times are known and the sampling clock is free running at a constant rate, i.e., the sampling clock is not phase locked to the symbol clock. Degradations in the output signal to noise ratio of the digital implementation due to sampling rate, sampling offset, and finite bandwidth, resulting from the anti-aliasing low pass prefilter, are computed and compared with those of the analog counterpart. It is shown that the digital IDF performs within 0.6 dB of the ideal analog IDF whenever the prefilter bandwidth exceeds four times the symbol rate and when sampling is performed at the Nyquist rate. The loss can be reduced to 0.3 dB by doubling the sampling rate, where 0.2 dB loss results from finite bandwidth and 0.1 dB results from the digital IDF.

Sadr, R.↗

NASA NTRS1987

On the choice of orbits for an altimetric satellite to study ocean circulation and tides

The choice of an orbit for satellite altimetric studies of the ocean's circulation and tides requires an understanding of the orbital characteristics that influence the accuracy of the satellite's measurements of sea level and the temporal and spatial distribution of the measurements. The orbital characteristics that influence accurate calculations of the satellite's position as a function of time are examined, and the pattern of ground tracks laid down on the ocean's surface as a function of the satellite's altitude and inclination is studied. The results are used to examine the aliases in the measurements of surface geostrophic currents and tides. Finally, these considerations are used to specify possible orbits that may be useful for the upcoming Topex/Poseidon mission.

Parke, Michael E.↗

NASA NTRS1987

Efficiency of a model human image code

Hypothetical schemes for neural representation of visual information can be expressed as explicit image codes. Here, a code modeled on the simple cells of the primate striate cortex is explored. The Cortex transform maps a digital image into a set of subimages (layers) that are bandpass in spatial frequency and orientation. The layers are sampled so as to minimize the number of samples and still avoid aliasing. Samples are quantized in a manner that exploits the bandpass contrast-masking properties of human vision. The entropy of the samples is computed to provide a lower bound on the code size. Finally, the image is reconstructed from the code. Psychophysical methods are derived for comparing the original and reconstructed images to evaluate the sufficiency of the code. When each resolution is coded at the threshold for detection artifacts, the image-code size is about 1 bit/pixel.

Watson, Andrew B.↗

NASA NTRS1988

Improvements to photometry. Part 1: Better estimation of derivatives in extinction and transformation equations

Atmospheric extinction in wideband photometry is examined both analytically and through numerical simulations. If the derivatives that appear in the Stromgren-King theory are estimated carefully, it appears that wideband measurements can be transformed to outside the atmosphere with errors no greater than a millimagnitude. A numerical analysis approach is used to estimate derivatives of both the stellar and atmospheric extinction spectra, avoiding previous assumptions that the extinction follows a power law. However, it is essential to satify the requirements of the sampling theorem to keep aliasing errors small. Typically, this means that band separations cannot exceed half of the full width at half-peak response. Further work is needed to examine higher order effects, which may well be significant.

Young, Andrew T.↗

NASA NTRS1989

Model-based quantification of image quality

In 1982, Park and Schowengerdt published an end-to-end analysis of a digital imaging system quantifying three principal degradation components: (1) image blur - blurring caused by the acquisition system, (2) aliasing - caused by insufficient sampling, and (3) reconstruction blur - blurring caused by the imperfect interpolative reconstruction. This analysis, which measures degradation as the square of the radiometric error, includes the sample-scene phase as an explicit random parameter and characterizes the image degradation caused by imperfect acquisition and reconstruction together with the effects of undersampling and random sample-scene phases. In a recent paper Mitchell and Netravelli displayed the visual effects of the above mentioned degradations and presented subjective analysis about their relative importance in determining image quality. The primary aim of the research is to use the analysis of Park and Schowengerdt to correlate their mathematical criteria for measuring image degradations with subjective visual criteria. Insight gained from this research can be exploited in the end-to-end design of optical systems, so that system parameters (transfer functions of the acquisition and display systems) can be designed relative to each other, to obtain the best possible results using quantitative measurements.

Hazra, Rajeeb↗

NASA NTRS1989

The role of topography in geodetic gravity field modelling

Masses associated with the topography, bathymetry, and its isostatic compensation are a dominant source of gravity field variations, especially at shorter wavelengths. On global scales the topographic/isostatic effects are also significant, except for the lowest harmonics. In practice, though, global effects need not be taken into account as such effects are included in the coefficients of the geopotential reference fields. On local scales, the short-wavelength gravity variations due to the topography may, in rugged terrain, be an order of magnitude larger than other effects. In such cases, explicit or implicit terrain reduction procedures are mandatory in order to obtain good prediction results. Such effects may be computed by space-domain integration or by fast Fourier transformation (FFT) methods. Numerical examples are given for areas of the Canadian Rockies. In principle, good knowledge of the topographic densities is required to produce the smoothest residual field. Densities may be determined from sample measurements or by gravimetric means, but both are somewhat troublesome methods in practice. The use of a standard density, e.g., 2.67 g/cu cm, may often yield satisfactory results and may be put within a consistent theoretical framework. The independence of density assumptions is the key point of the classical Molodensky approach to the geodetic boundary value problem. The Molodensky solutions take into account that land gravity field observations are done on a non-level surface. Molodensky's problem may be solved by integral expansions or more effective FFT methods, but the solution should not be intermixed with the use of terrain reductions. The methods are actually complimentary and may both be required in order to obtain the smoothest possible signal, least prone to aliasing and other effects coming from sparse data coverage, typical of rugged topography.

Forsberg, R.↗

NASA NTRS1990

An in-flight interaction of the X-29A canard and flight control system

Many of today's high performance airplanes use high gain, digital flight control systems. These sytems are liable to couple with the aircraft's structural dynamics and aerodynamics to cause an aeroservoelastic interaction. These interactions can be stable or unstable depending upon damping and phase relationships within the system. The details of an aeroservoelastic interaction experienced in flight by the X-29A forward-swept wing airplane. A 26.5-Hz canard pitch mode response was aliased by the digital sampling rate in the canard position feedback loop of the flight control system, resulting in a 13.5-Hz signal being commanded to the longitudinal control surfaces. The amplitude of this commanded signal increased as the wear of the canard seals increased, as the feedback path gains were increased, and as the canard aerodynamic loading decreased. The resultant control surface deflections were of sufficient amplitude to excite the structure. The flight data presented shows the effect of each component (structural dynamics, aerodynamics, and flight control system) for this aeroservoelastic interaction.

Kehoe, Michael W.↗

NASA NTRS1990

Local spatial frequency analysis for computer vision

A sense of vision is a prerequisite for a robot to function in an unstructured environment. However, real-world scenes contain many interacting phenomena that lead to complex images which are difficult to interpret automatically. Typical computer vision research proceeds by analyzing various effects in isolation (e.g., shading, texture, stereo, defocus), usually on images devoid of realistic complicating factors. This leads to specialized algorithms which fail on real-world images. Part of this failure is due to the dichotomy of useful representations for these phenomena. Some effects are best described in the spatial domain, while others are more naturally expressed in frequency. In order to resolve this dichotomy, we present the combined space/frequency representation which, for each point in an image, shows the spatial frequencies at that point. Within this common representation, we develop a set of simple, natural theories describing phenomena such as texture, shape, aliasing and lens parameters. We show these theories lead to algorithms for shape from texture and for dealiasing image data. The space/frequency representation should be a key aid in untangling the complex interaction of phenomena in images, allowing automatic understanding of real-world scenes.

Krumm, John↗

NASA NTRS1989

Periodic solar EUV flux monitored near Venus

A detector sharing the orbital rate of Venus has a unique perspective on solar periodicities. Fourier analysis of the 8.6 year record of solar EUV output gathered by the Langmuir probe on Pioneer Venus Orbiter shows the influences of global oscillation modes located in the convective envelope and in the radiative interior. Seven of the eight lowest angular harmonic r-mode familes are detected by their rotation rates which differ almost unmeasurably from ideal theoretical values. This determines a mean sidereal rotation rate for the envelope of 457.9 + or - 2.0 nHz which corresponds to a period of 25.3 days. Many frequencies are aliased at + or - 106 nHz by modulation from the lowest angular harmonic r-mode in the envelope.

Wolff, Charles L.↗

NASA NTRS1990

An in-flight interaction of the X-29A canard and flight control system

This paper presents the details of an aeroservoelastic interaction experienced in flight by the X-29A forward-swept-wing aircraft. A 26.5-Hz canard pitch-mode response was aliased by the digital sampling rate in the canard-position feed-back loop of the flight-control system, resulting in a 13.5-Hz signal being commanded to the longitudinal control surfaces. The amplitude of this commanded signal increased as the wear of the canard seals increased, as the feedback path gains were increased, and as the canard aerodynamic loading decreased. The resultant control-surface deflections were of sufficient amplitude to excite the structure. The flight data presented shows the effect of each component (structural dynamics, aerodynamics, and flight-control system) for this aeroservoelastic interaction.

Kehoe, Michael W.↗

NASA NTRS1989

Analysis of a parallel multigrid algorithm

This paper considers the parallel multigrid algorithm of Frederickson and McBryan (1987). This algorithm uses multiple coarse-grid problems (instead of one) in the hope of accelerating convergence, and is found to have a close relationship to traditional multigrid methods. Specifically, the parallel coarse-grid correction operator is identical to a traditional multigrid coarse-grid correction operator, except that the mixing of high and low frequencies caused by aliasing error is removed. Appropriate relaxation operators can be chosen to take advantage of this property. Comparisons between the standard multigrid and the new method are made.

Chan, Tony F.↗

NASA NTRS1990

A comparison of ship and Coastal Zone Color Scanner mapped distribution of phytoplankton in the southeastern Bering Sea

Twenty-one Coastal Zone Color Scanner (CZCS) images of the southeastern Bering Sea are examined in order to map the near-surface distribution of phytoplankton during 1979 and 1980. The information is compared with the mesoscale (100-1000 km) distribution of phytoplankton inferred from pooled ship sampling obtained during the Processes and Resources of the Bering Shelf (PROBES) intensive field study during the late 1970s and early 1980s. The imagery indicates that open-water phytoplankton blooms occur first in late April in coastal waters, peak in early May over the middle shelf, and decay rapidly afterwards, reaching concentration minima in June in both regions. These patterns show that the earlier ship observations are valid for most of the eastern Bering shelf. A very tight correlation is found between the PROBES surface chlorophyll a concentrations and mean mixed-layer chlorophyll concentrations. The significant discrepancies between CZCS and ship-based chlorophyll estimates may be due to aliasing in time by the CZCS. It is concluded that neither satellite nor ship alone can do an adequate job of characterizing the physics or biological dynamics of the ocean.

Mcclain, C. R.↗

NASA NTRS1991

Design and status of the RF-digitizer integrated circuit

An integrated circuit currently under development samples a bandpass-limited signal at a radio frequency in quadrature and then performs a simple sum-and-dump operation in order to filter and lower the rate of the samples. Downconversion to baseband is carried out by the sampling step itself through the aliasing effect of an appropriately selected subharmonic sampling frequency. Two complete RF digitizer circuits with these functions will be implemented with analog and digital elements on one GaAs substrate. An input signal, with a carrier frequency as high as 8 GHz, can be sampled at a rate as high as 600 Msamples/sec for each quadrature component. The initial version of the chip will sign-sample (1-bit) the input RF signal. The chip will contain a synthesizer to generate a sample frequency that is a selectable integer multiple of an input reference frequency. In addition to the usual advantages of compactness and reliability associated with integrated circuits, the single chip will replace several steps required by standard analog downconversion. Furthermore, when a very high initial sample rate is selected, the presampling analog filters can be given very large bandwidths, thereby greatly reducing phase and delay instabilities typically introduced by such filters, as well as phase and delay variation due to Doppler changes.

Rayhrer, B.↗

NASA NTRS1991

Image gathering and digital restoration for fidelity and visual quality

The fidelity and resolution of the traditional Wiener restorations given in the prevalent digital processing literature can be significantly improved when the transformations between the continuous and discrete representations in image gathering and display are accounted for. However, the visual quality of these improved restorations also is more sensitive to the defects caused by aliasing artifacts, colored noise, and ringing near sharp edges. In this paper, these visual defects are characterized, and methods for suppressing them are presented. It is demonstrated how the visual quality of fidelity-maximized images can be improved when (1) the image-gathering system is specifically designed to enhance the performance of the image-restoration algorithm, and (2) the Wiener filter is combined with interactive Gaussian smoothing, synthetic high edge enhancement, and nonlinear tone-scale transformation. The nonlinear transformation is used primarily to enhance the spatial details that are often obscurred when the normally wide dynamic range of natural radiance fields is compressed into the relatively narrow dynamic range of film and other displays.

Huck, Friedrich O.↗