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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Reproducible Growth of High-Quality Cubic-SiC Layers

Semiconductor electronic devices and circuits based on silicon carbide (SiC) are being developed for use in high-temperature, high-power, and/or high-radiation conditions under which devices made from conventional semiconductors cannot adequately perform. The ability of SiC-based devices to function under such extreme conditions is expected to enable significant improvements in a variety of applications and systems. These include greatly improved high-voltage switching for saving energy in public electric power distribution and electric motor drives; more powerful microwave electronic circuits for radar and communications; and sensors and controls for cleaner-burning, more fuel-efficient jet aircraft and automobile engines.

Neudeck, Philip G.↗
NASA NTRS2016

Sampling for Soil Carbon Stock Assessment in Rocky Agricultural Soils

Coring methods commonly employed in soil organic C (SOC) stock assessment may not accurately capture soil rock fragment (RF) content or soil bulk density (rho (sub b)) in rocky agricultural soils, potentially biasing SOC stock estimates. Quantitative pits are considered less biased than coring methods but are invasive and often cost-prohibitive. We compared fixed-depth and mass-based estimates of SOC stocks (0.3-meters depth) for hammer, hydraulic push, and rotary coring methods relative to quantitative pits at four agricultural sites ranging in RF content from less than 0.01 to 0.24 cubic meters per cubic meter. Sampling costs were also compared. Coring methods significantly underestimated RF content at all rocky sites, but significant differences (p is less than 0.05) in SOC stocks between pits and corers were only found with the hammer method using the fixed-depth approach at the less than 0.01 cubic meters per cubic meter RF site (pit, 5.80 kilograms C per square meter; hammer, 4.74 kilograms C per square meter) and at the 0.14 cubic meters per cubic meter RF site (pit, 8.81 kilograms C per square meter; hammer, 6.71 kilograms C per square meter). The hammer corer also underestimated rho (sub b) at all sites as did the hydraulic push corer at the 0.21 cubic meters per cubic meter RF site. No significant differences in mass-based SOC stock estimates were observed between pits and corers. Our results indicate that (i) calculating SOC stocks on a mass basis can overcome biases in RF and rho (sub b) estimates introduced by sampling equipment and (ii) a quantitative pit is the optimal sampling method for establishing reference soil masses, followed by rotary and then hydraulic push corers.

hammer method↗
NASA NTRS2012

Characteristics and Composition of Atmospheric Aerosols in Phimai, Central Thailand During BASE-ASIA

Popular summary: Atmospheric aerosols play an important role in the Earth's climate system, and can also have adverse effects on air quality and human health. The environmental impacts of aerosols, on the other hand, are highly regional, since their temporal/spatial distribution is inhomogeneous and highly depends on the regional emission sources. To better understand the effects of aerosols, intensive field experiments are necessary to characterize the chemical and physical properties on a region-by-region basis. From late February to early May in 2006, NASA/GSFC's SMARTLabs facility was deployed at a rural site in central Thailand, Southeast Asia, to conduct a field experiment dubbed BASE-ASIA (Biomass-burning Aerosols in South East-Asia: Smoke Impact Assessment). The group was joined by scientists from the University of Hawaii and other regional institutes. Comprehensive measurements were made during the experiment, including aerosol chemical composition, optical and microphysical properties, as well as surface energetics and local . meteorology. This study analyzes part of the data from the BASE-ASIA experiment. It was found that, even for the relatively remote rural site, the aerosol loading was still substantial. Besides agricultural burning in the area, industrial pollution near the Bangkok metropolitan area, about 200 km southeast of the site, and even long-range transport from China, also contribute to the area's aerosol loading. The results indicate that aerosol pollution has developed into a regional problem for northern Indochina, and may become more severe as the region's population and economy continue to grow. Abstract: Comprehensive measurements of atmospheric aerosols were made in Phimai, central Thailand (15.l83 N, 102.565 E, elevation: 206 m) during the BASE-ASIA field experiment from late February to early May in 2006. The observed aerosol loading was sizable for this rural site (mean aerosol scattering: 108 +/- 64 Mm(exp -1); absorption: 15 +/- 8 Mm(exp -1); PM(sub 10) concentration: 33 +/- 17 miro-g/ cubic m and dominated by submicron particles. Major aerosol compounds included carbonaceous (OC: 9.5 +/- 3.6miro-g/ cubic m; EC: 2.0 2.3 miro-g/ cubic m and secondary species (SO4(2-): 6.4 +/- 3.7 miro-g/ cubic m, NH4(+): 2.2 +/- 1.3 miro-g/ cubic m). While the site was seldom under the direct influence of large forest fires to its north, agricultural fires were ubiquitous during the experiment, as suggested by the substantial concentration of K+ (0.56 +/- 0.33 micro-g/ cubic m). Besides biomass burning, aerosols in Phimai during the experiment were also strongly influenced by industrial and vehicular emissions from the Bangkok metropolitan region and long-range transport from southern China. High humidity played an important role in determining the aerosol composition and properties in the region. Sulfate was primarily formed via aqueous phase reactions, and hygroscopic growth could enhance the aerosol light scattering by up to 60%, at the typical morning RH level of 85%. The aerosol single scattering albedo demonstrated distinct diurnal variation, ranging from 0.86 +/- 0.04 in the evening to 0.92 +/- 0.02 in the morning. This experiment marks the first time such comprehensive characterization of aerosols was made for rural central Thailand. Our results indicate that aerosol pollution has developed into a regional problem for northern Indochina, and may become more severe as the region's population and economy continue to grow.

Li, Can↗
NASA NTRS2015

Thermal Conductivity and Erosion Durability of Composite Two-Phase Air Plasma Sprayed Thermal Barrier Coatings

To enhance efficiency of gas turbines, new thermal barrier coatings (TBCs) must be designed which improve upon the thermal stability limit of 7 wt% yttria stabilized zirconia (7YSZ), approximately 1200 C. This tenant has led to the development of new TBC materials and microstructures capable of improved high temperature performance. This study focused on increasing the erosion durability of cubic zirconia based TBCs, traditionally less durable than the metastable t' zirconia based TBCs. Composite TBC microstructures composed of a low thermal conductivity/high temperature stable cubic Low-k matrix phase and a durable t' Low-k secondary phase were deposited via APS. Monolithic coatings composed of cubic Low-k and t' Low-k were also deposited, in addition to a 7YSZ benchmark. The thermal conductivity and erosion durability were then measured and it was found that both of the Low-k materials have significantly reduced thermal conductivities, with monolithic t' Low-k and cubic Low-k improving upon 7YSZ by approximately 13 and approximately 25%, respectively. The 40 wt% t' Low-k composite (40 wt% t' Low-k - 60 wt% cubic Low-k) showed a approximately 22% reduction in thermal conductivity over 7YSZ, indicating even at high levels, the t' Low-k secondary phase had a minimal impact on thermal in the composite coating. It was observed that a mere 20 wt% t' Low-k phase addition can reduce the erosion of a cubic Low-k matrix phase composite coating by over 37%. Various mixing rules were then investigated to assess this non-linear composite behavior and suggestions were made to further improve erosion durability.

Rare earth zirconia↗
NASA NTRS2016

Soil Moisture Active Passive Mission L4_SM Data Product Assessment (Version 2 Validated Release)

During the post-launch SMAP calibration and validation (Cal/Val) phase there are two objectives for each science data product team: 1) calibrate, verify, and improve the performance of the science algorithm, and 2) validate the accuracy of the science data product as specified in the science requirements and according to the Cal/Val schedule. This report provides an assessment of the SMAP Level 4 Surface and Root Zone Soil Moisture Passive (L4_SM) product specifically for the product's public Version 2 validated release scheduled for 29 April 2016. The assessment of the Version 2 L4_SM data product includes comparisons of SMAP L4_SM soil moisture estimates with in situ soil moisture observations from core validation sites and sparse networks. The assessment further includes a global evaluation of the internal diagnostics from the ensemble-based data assimilation system that is used to generate the L4_SM product. This evaluation focuses on the statistics of the observation-minus-forecast (O-F) residuals and the analysis increments. Together, the core validation site comparisons and the statistics of the assimilation diagnostics are considered primary validation methodologies for the L4_SM product. Comparisons against in situ measurements from regional-scale sparse networks are considered a secondary validation methodology because such in situ measurements are subject to up-scaling errors from the point-scale to the grid cell scale of the data product. Based on the limited set of core validation sites, the wide geographic range of the sparse network sites, and the global assessment of the assimilation diagnostics, the assessment presented here meets the criteria established by the Committee on Earth Observing Satellites for Stage 2 validation and supports the validated release of the data. An analysis of the time average surface and root zone soil moisture shows that the global pattern of arid and humid regions are captured by the L4_SM estimates. Results from the core validation site comparisons indicate that "Version 2" of the L4_SM data product meets the self-imposed L4_SM accuracy requirement, which is formulated in terms of the ubRMSE: the RMSE (Root Mean Square Error) after removal of the long-term mean difference. The overall ubRMSE of the 3-hourly L4_SM surface soil moisture at the 9 km scale is 0.035 cubic meters per cubic meter requirement. The corresponding ubRMSE for L4_SM root zone soil moisture is 0.024 cubic meters per cubic meter requirement. Both of these metrics are comfortably below the 0.04 cubic meters per cubic meter requirement. The L4_SM estimates are an improvement over estimates from a model-only SMAP Nature Run version 4 (NRv4), which demonstrates the beneficial impact of the SMAP brightness temperature data. L4_SM surface soil moisture estimates are consistently more skillful than NRv4 estimates, although not by a statistically significant margin. The lack of statistical significance is not surprising given the limited data record available to date. Root zone soil moisture estimates from L4_SM and NRv4 have similar skill. Results from comparisons of the L4_SM product to in situ measurements from nearly 400 sparse network sites corroborate the core validation site results. The instantaneous soil moisture and soil temperature analysis increments are within a reasonable range and result in spatially smooth soil moisture analyses. The O-F residuals exhibit only small biases on the order of 1-3 degrees Kelvin between the (re-scaled) SMAP brightness temperature observations and the L4_SM model forecast, which indicates that the assimilation system is largely unbiased. The spatially averaged time series standard deviation of the O-F residuals is 5.9 degrees Kelvin, which reduces to 4.0 degrees Kelvin for the observation-minus-analysis (O-A) residuals, reflecting the impact of the SMAP observations on the L4_SM system. Averaged globally, the time series standard deviation of the normalized O-F residuals is close to unity, which would suggest that the magnitude of the modeled errors approximately reflects that of the actual errors. The assessment report also notes several limitations of the "Version 2" L4_SM data product and science algorithm calibration that will be addressed in future releases. Regionally, the time series standard deviation of the normalized O-F residuals deviates considerably from unity, which indicates that the L4_SM assimilation algorithm either over- or under-estimates the actual errors that are present in the system. Planned improvements include revised land model parameters, revised error parameters for the land model and the assimilated SMAP observations, and revised surface meteorological forcing data for the operational period and underlying climatological data. Moreover, a refined analysis of the impact of SMAP observations will be facilitated by the construction of additional variants of the model-only reference data. Nevertheless, the “Version 2” validated release of the L4_SM product is sufficiently mature and of adequate quality for distribution to and use by the larger science and application communities.

SMAP L4_SM↗
NASA NTRS2016

Variation in Global Chemical Composition of PM2.5: Emerging Results from SPARTAN

The Surface PARTiculate mAtter Network (SPARTAN) is a long-term project that includes characterization of chemical and physical attributes of aerosols from filter samples collected worldwide. This paper discusses the ongoing efforts of SPARTAN to define and quantify major ions and trace metals found in fine particulate matter (PM (sub 2.5). Our methods infer the spatial and temporal variability of PM (sub 2.5) in a cost-effective manner. Gravimetrically weighed filters represent multi-day averages of PM (sub 2.5), with a collocated nephelometer sampling air continuously. SPARTAN instruments are paired with AErosol RObotic NETwork (AERONET) sun photometers to better understand the relationship between ground-level PM (sub 2.5) and columnar aerosol optical depth (AOD). We have examined the chemical composition of PM (sub 2.5) at 12 globally dispersed, densely populated urban locations and a site at Mammoth Cave (US) National Park used as a background comparison. So far, each SPARTAN location has been active between the years 2013 and 2016 over periods of 2-26 months, with an average period of 12 months per site. These sites have collectively gathered over 10 years of quality aerosol data. The major PM (sub 2.5) constituents across all sites (relative contribution plus or minus Standard Deviation) are ammoniated sulfate (20 percent plus or minus 11 percent), crustal material (13.4 percent plus or minus 9.9 percent), equivalent black carbon (11.9 percent plus or minus 8.4 percent), ammonium nitrate (4.7 percent plus or minus 3.0 percent), sea salt (2.3 percent plus or minus 1.6 percent), trace element oxides (1.0 percent plus or minus 1.1 percent), water (7.2 percent plus or minus 3.3 percent) at 35 percent relative humidity, and residual matter (40 percent plus or minus 24 percent). Analysis of filter samples reveals that several PM (sub 2.5) chemical components varied by more than an order of magnitude between sites. Ammoniated sulfate ranges from 1.1 microns per cubic meter (Buenos Aires, Argentina) to 17 microns per cubic meter (Kanpur, India in the dry season). Ammonium nitrate ranged from 0.2 microns per cubic meter (Mammoth Cave, in summer) to 6.8 microns per cubic meter (Kanpur, dry season). Equivalent black carbon ranged from 0.7 microns per cubic meter (Mammoth Cave) to over 8 microns per cubic meter (Dhaka, Bangladesh and Kanpur, India). Comparison of SPARTAN vs. coincident measurements from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network at Mammoth Cave yielded a high degree of consistency for daily PM (sub 2.5) (r squared equals 0.76, slope equals 1.12), daily sulfate (r squared equals 0.86, slope equals 1.03), and mean fractions of all major PM (sub 2.5) components (within 6 percent). Major ions generally agree well with previous studies at the same urban locations (e.g. sulfate fractions agree within 4 percent for 8 out of 11 collocation comparisons). Enhanced anthropogenic dust fractions in large urban areas (e.g. Singapore, Kanpur, Hanoi, and Dhaka) are apparent from high Zn to Al ratios. The expected water contribution to aerosols is calculated via the hygroscopicity parameter kappa (sub v (volume)) for each filter. Mean aggregate values ranged from 0.15 (Ilorin) to 0.28 (Rehovot). The all-site parameter mean is 0.20 plus or minus 0.04. Chemical composition and water retention in each filter measurement allows inference of hourly PM (sub 2.5) at 35 percent relative humidity by merging with nephelometer measurements. These hourly PM (sub 2.5) estimates compare favourably with a beta attenuation monitor (MetOne) at the nearby US embassy in Beijing, with a coefficient of variation r squared equals 0.67 (number equals 3167), compared to r squared equals 0.62 when v (volume) was not considered. SPARTAN continues to provide an open-access database of PM (sub 2.5) compositional filter information and hourly mass collected from a global federation of instruments.

Snider, Graydon↗
NASA NTRS1987

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗
NASA NTRS1986

Efficient inverse solution of Kepler's equation

A bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.

Boltz, Frederick W.↗
NASA NTRS2002

Cloud Condensation Nuclei Measurements in Tropical Cyclones

The first measurements of cloud condensation nuclei (CCN) within and around tropical cyclones were made with the Desert Research Institute (DRI) CCN spectrometer (Hudson 1909) from a NOAA P-3 Hurricane Hunter aircraft throughout the 2001 season. Two penetrations of the closed eye of Hurricane Erin off the northeast US coast on Sept. 10 showed concentrations consistently well in excess of 1000 per cubic cm at approximately 1.4% supersaturation. Simultaneous condensation nuclei (CN--total particle) concentrations were consistently well in excess of 2000 per cubic cm throughout these closed eye penetrations. These within eye measurements at 4 km altitude for exceeded CCN and CN measurements just outside of the storm at similar altitudes--300 and 600 per cubic cm respectively. These CCN and CN concentrations within this closed eye were far above concentrations in maritime air masses; they are characteristic of continental or polluted air masses. Although there was a possibility that Saharan duct may have gotten into this storm these sub tenth micrometer particles are much too small and much too numerous to be dust. Such high concentrations may have originated from European air pollution, which may have been transported by similar airflow patterns to those that carry Saharan dust across the Atlantic. These high concentrations may be a manifestation of descending air that brings higher concentrations that are often characteristic of the upper troposphere (Clarke and Kapustin 2002). Later in the month measurements in Humberto showed highly variable CCN and CN concentrations that ranged from lots than 5 per cubic cm to more than 1000 per Cubic cm over km scale distances within and around the open eye of this tropical storm/hurricane. These very low concentrations suggest strong cloud scavenging.

Hudson, J. G.↗
NASA NTRS2005

Neutron Diffraction Study Oxygen Dissolution Alpha(sub 2)-Ti3Al

Rietveld refinements of neutron powder diffraction data on alpha(sub 2)-Ti3Al have been performed to determine the crystal structure as a function of interstitial oxygen (O) concentration for three alloys with a Ti/Al ratio of approximately equal to 2.34 and O concentrations of 0.25%, 3.99% and 7.71%. The structures of the allows are hexagonal in space group P6(sub 3)/mmc where Ti and Al atoms populate unique sites with excess Al at the Ti site and O atoms occupy octahedral interstitial sites surrounded by six Ti sites. The length of the c-axis was found to increase linearly as the O occupancy of the interstitial sites increased; this lattice lengthening effect was much less pronounced along the alpha axis. Correspondingly, the increases in the lengths of Ti-Al and Ti-Ti bonds with a major component of their direction parallel to the c-axis were roughly an order of magnitude greater than the increases in the lengths of Ti-al and Ti-Ti bonds more closely aligned with the alpha-axis. Densities calculated form the lattice parameters and occupancy factors fall in the range (4.118 plus or minus 0.004) grams per cubic centimeter to (4.194 plus or minus 0.004) grams per cubic centimeter, and exhibit a nearly linear increase with oxygen concentration. Measured densities of (4.113 plus or minus 0.001) grams per cubic centimeter, (4.146 plus or minus 0.009) grams per cubic centimeter, and (4.191 plus or minus 0.002) grams per cubic centimeter for these alloys agree with the results of the refinements.

Jones, Camille Y.↗
NASA NTRS2009

Lattice-Matched Semiconductor Layers on Single Crystalline Sapphire Substrate

SiGe is an important semiconductor alloy for high-speed field effect transistors (FETs), high-temperature thermoelectric devices, photovoltaic solar cells, and photon detectors. The growth of SiGe layer is difficult because SiGe alloys have different lattice constants from those of the common Si wafers, which leads to a high density of defects, including dislocations, micro-twins, cracks, and delaminations. This innovation utilizes newly developed rhombohedral epitaxy of cubic semiconductors on trigonal substrates in order to solve the lattice mismatch problem of SiGe by using trigonal single crystals like sapphire (Al2O3) as substrate to give a unique growth-orientation to the SiGe layer, which is automatically controlled at the interface upon sapphire (0001). This technology is different from previous silicon on insulator (SOI) or SGOI (SiGe on insulator) technologies that use amorphous SiO2 as the growth plane. A cubic semiconductor crystal is a special case of a rhombohedron with the inter-planar angle, alpha = 90 deg. With a mathematical transformation, all rhombohedrons can be described by trigonal crystal lattice structures. Therefore, all cubic lattice constants and crystal planes (hkl) s can be transformed into those of trigonal crystal parameters. These unique alignments enable a new opportunity of perfect lattice matching conditions, which can eliminate misfit dislocations. Previously, these atomic alignments were thought to be impossible or very difficult. With the invention of a new x-ray diffraction measurement method here, growth of cubic semiconductors on trigonal crystals became possible. This epitaxy and lattice-matching condition can be applied not only to SiGe (111)/sapphire (0001) substrate relations, but also to other crystal structures and other materials, including similar crystal structures which have pointgroup rotational symmetries by 120 because the cubic (111) direction has 120 rotational symmetry. The use of slightly miscut (less than plus or minus 10 deg.) sapphire (0001) substrate can be used to improve epitaxial relationships better by providing attractive atomic steps in the epitaxial process.

Choi, Sang↗
NASA NTRS1977

Resampling study

The author has identified the following significant results. The nearest neighbor and cubic convolution resampling algorithms were applied to a variety of images extracted from LANDSAT MSS data. A comparison of the results demonstrated that (1) cubic convolution can cause spreading of small features and can introduce noticeable overshoot (ringing) into the data; (2) cubic convolution attenuates the high spatial frequencies compared to the original and nearest neighbor resampled data; and (3) cubic convolution generally produces photographic products of superior visual quality. The effects of the resampling algorithms on multispectral classification were not conclusively determined due to the small number of images tested.

Ferneyhough, D. G.↗
NASA NTRS1981

Theory, computation, and application of exponential splines

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mccartin, B. J.↗
NASA NTRS1987

Hydrogen trapping and the interaction of hydrogen with metals

A method has been developed for the determination of trapped hydrogen in metal alloys, involving the determination of mobile hydrogen using the electrochemical method and the determination of total hydrogen with the fusion method, the difference in hydrogen concentrations being due to trapped hydrogen. It has been found that hydrogen enters body-centered cubic structures through the grain bodies rather than through the grain boundaries. Hydrogen also diffuses much more rapidly in body-centered cubic structures on charging than in face-centered cubic structures, the hydrogen distribution being more uniform in nature. The energy necessary to cause hydrogen embrittlement is postulated to arise from the changes in crystal lattice energies brought about through interaction of hydrogen with atoms in the metal lattice. The total energy change is more negative for body-centered cubic structures, believed to be the cause of a greater tendency toward hydrogen embrittlement. Finally, the agreement of hydrogen concentrations obtained at 25 C by the electrochemical method with those obtained by the fusion method are taken as a strong indication of the power and validity of the electrochemical method.

Danford, Merlin D.↗
NASA NTRS1986

Spectral analysis of linear, shift-invariant interpolants

The use of a spectral analysis technique to evaluate the reconstruction/interpolation performance of linear, shift-invariant interpolants is examined. The technique was utilized to measure the performance of cubic hermite, quintic hermite, exponential, cubic, spline, Nu, PCC, Keys cubic, and BAWA cubic interpolants. The performance criterion is based upon the mean square error of the difference between the sampled and reconstructed functions. The reconstruction properties, interpolation functions, and reconstruction filters for the interpolants are studied and compared. It is noted that the spectral analysis technique is applicable to reconstruction algorithms used in signal and image processes, and interpolants used in numerical analysis, computer-aided design, and computer graphics.

Lansing, Donald L.↗