Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Phase transformations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Shock-induced transition of quartz to stishovite.

The transformation of quartz to stishovite has been studied by X-ray and optical examination of a series of experimentally shock-loaded specimens of a quartz-copper mixture. Shock pressures of 68 to 260 kb and peak temperatures of 320 to 870 K were achieved. Stishovite was identified from quartz shock-loaded above 90 kb; the quantity increases with increasing pressure, but is not dependent on temperature. The formation of stishovite under shock conditions appears to be intimately related to a short-range order phase.

Kleeman, J. D.↗
NASA NTRS1987

Oxygen measurements in thin ribbon silicon

The oxygen content of thin silicon ribbons grown by the dendritic web technique was measured using a modification of the ASTM method based on Fourier transform infrared spectroscopy. Web silicon was found to have a high oxygen content, ranging from 13 to 19 ppma, calculated from the absorption peak associated with interstitial oxygen and using the new ASTM conversion coefficient. The oxygen concentration changed by about 10 percent along the growth direction of the ribbon. In some samples, a shoulder was detected on the absorption peak. A similar shoulder in Czochralski grown material has been variously interpreted in the literature as due to a complex of silicon, oxygen, and vacancies, or to a phase of SiO2 developed along dislocations in the material. In the case of web silicon, it is not clear which is the correct interpretation.

Hyland, S. L.↗
NASA NTRS1994

Direct measurement of free-energy barrier to nucleation of crystallites in amorphous silicon thin films

A method is introduced to measure the free-energy barrier W(sup *), the activation energy, and activation entropy to nucleation of crystallites in amorphous solids, independent of the energy barrier to growth. The method allows one to determine the temperature dependence of W(sup *), and the effect of the preparation conditions of the initial amorphous phase, the dopants, and the crystallization methds on W(sup *). The method is applied to determine the free-energy barrier to nucleation of crystallites in amorphous silicon (a-Si) thin films. For thermally induced nucleation in a-Si thin films with annealing temperatures in the range of from 824 to 983 K, the free-energy barrier W(sup *) to nucleation of silicon crystals is about 2.0 - 2.1 eV regardless of the preparation conditions of the films. The observation supports the idea that a-Si transforms into an intermediate amorphous state through the structural relaxation prior to the onset of nucleation of crystallites in a-Si. The observation also indicates that the activation entropy may be an insignificant part of the free-energy barrier for the nucleation of crystallites in a-Si. Compared with the free-energy barrier to nucleation of crystallites in undoped a-Si films, a significant reduction is observed in the free-energy barrier to nucleation in Cu-doped a-Si films. For a-Si under irradiation of Xe(2+) at 10(exp 5) eV, the free-energy barrier to ion-induced nucleation of crystallites is shown to be about half of the value associated with thermal-induced nucleation of crystallites in a-Si under the otherwise same conditions, which is much more significant than previously expected. The present method has a general kinetic basis; it thus should be equally applicable to nucleation of crystallites in any amorphous elemental semiconductors and semiconductor alloys, metallic and polymeric glasses, and to nucleation of crystallites in melts and solutions.

Shi, Frank G.↗
NASA NTRS1978

Experimental clean combustor program: Phase 3: Turbulence measurement addendum

Airflow turbulence parameters were measured in the high pressure, high temperature flow stream leaving the compressor of an operating gas turbine engine. A water cooled hot film turbulence probe was used to determine the turbulence intensity and length scale in the compressor exit flow stream of the CF6-50 engine. Data were obtained only at idle operating conditions. At engine power levels above idle conditions, durability problems and erratic data readings were encountered with the turbulence measurement probes. Turbulence measurements were made at three radial immersions at a point 15.5 cm downstream of the compressor outlet guide vanes in the compressor exit diffuser. The passage height at this point is 5.54 cm. Data reduction was accomplished with a time-data fast Fourier transform (FFT) system. This system finds the power spectral density distribution (PSD) of a large number of data samples using a direct Fourier transform algorithm and finds the autocorrelation parameter for these data by doing an FFT analysis of the PSD curves for a series of time delay intervals.

Taylor, J. R.↗
NASA NTRS2014

Revised (Mixed-Effects) Estimation for Forest Burning Emissions of Gases and Smoke, Fire/Emission Factor Typology, and Potential Remote Sensing Classification of Types for Ozone and Black-Carbon Simulation

We summarize recent progress (a) in correcting biomass burning emissions factors deduced from airborne sampling of forest fire plumes, (b) in understanding the variability in reactivity of the fresh plumes sampled in ARCTAS (2008), DC3 (2012), and SEAC4RS (2013) airborne missions, and (c) in a consequent search for remotely sensed quantities that help classify forest-fire plumes. Particle properties, chemical speciation, and smoke radiative properties are related and mutually informative, as pictures below suggest (slopes of lines of same color are similar). (a) Mixed-effects (random-effects) statistical modeling provides estimates of both emission factors and a reasonable description of carbon-burned simultaneously. Different fire plumes will have very different contributions to volatile organic carbon reactivity; this may help explain differences of free NOx(both gas- and particle-phase), and also of ozone production, that have been noted for forest-fire plumes in California. Our evaluations check or correct emission factors based on sequential measurements (e.g., the Normalized Ratio Enhancement and similar methods). We stress the dangers of methods relying on emission-ratios to CO. (b) This work confirms and extends many reports of great situational variability in emissions factors. VOCs vary in OH reactivity and NOx-binding. Reasons for variability are not only fuel composition, fuel condition, etc., but are confused somewhat by rapid transformation and mixing of emissions. We use "unmixing" (distinct from mixed-effects) statistics and compare briefly to approaches like neural nets. We focus on one particularly intense fire the notorious Yosemite Rim Fire of 2013. In some samples, NOx activity was not so suppressed by binding into nitrates as in other fires. While our fire-typing is evolving and subject to debate, the carbon-burned delta(CO2+CO) estimates that arise from mixed effects models, free of confusion by background-CO2 variation, should provide a solid base for discussion. (c) We report progress using promising links we find between emissions-related "fire types" and promising features deducible from remote observations of plumes, e.g., single scatter albedo, Angstrom exponent of scattering, Angstrom exponent of absorption, (CO column density)/(aerosol optical depth).

Remote sensing↗
NASA NTRS1981

Vapor phase diamond growth technology

Ion beam deposition chambers used for carbon film generation were designed and constructed. Features of the developed equipment include: (1) carbon ion energies down to approx. 50 eV; (2) in suit surface monitoring with HEED; (3) provision for flooding the surface with ultraviolet radiation; (4) infrared laser heating of substrate; (5) residual gas monitoring; (6) provision for several source gases, including diborane for doping studies; and (7) growth from either hydrocarbon source gases or from carbon/argon arc sources. Various analytical techniques for characterization of from carbon/argon arc sources. Various analytical techniques for characterization of the ion deposited carbon films used to establish the nature of the chemical bonding and crystallographic structure of the films are discussed. These include: H2204/HN03 etch; resistance measurements; hardness tests; Fourier transform infrared spectroscopy; scanning auger microscopy; electron spectroscopy for chemical analysis; electron diffraction and energy dispersive X-ray analysis; electron energy loss spectroscopy; density measurements; secondary ion mass spectroscopy; high energy electron diffraction; and electron spin resonance. Results of the tests are summarized.

Angus, J. C.↗
NASA NTRS1987

Radial/axial power divider/combiner

An electromagnetic power divider/combiner comprises N radial outputs (31) having equal powers and preferably equal phases, and a single axial output (20). A divider structure (1) and a preferably identical combiner structure (2) are broadside coupled across a dielectric substrate (30) containing on one side the network of N radial outputs (31) and on its other side a set of N equispaced stubs (42) which are capacitively coupled through the dielectric substrate (30) to the N radial outputs (31). The divider structure (1) and the combiner structure (2) each comprise a dielectric disk (12, 22, respectively) on which is mounted a set of N radial impedance transformers (14, 24, respectively). Gross axial coupling is determined by the thickness of the dielectric layer (30). Rotating the disks (12, 22) with respect to each other effectuates fine adjustment in the degree of axial coupling.

Vaddiparty, Yerriah P.↗
NASA NTRS2024

SMAnalytics Automated Shape Memory Test Analysis Software User's Manual: UCFTC, UPER, and DSC Test Methods, Version 1.0.2

Over the course of 60 years of shape memory alloy research and development, the properties of these alloys have been measured using various testing methods, which are often customized by the organization performing the test. However, commercial adoption of shape memory alloys in aeronautic actuator applications requires reducing property uncertainty through standardizing test methods. Historically, differential scanning calorimetry (DSC) has been used to measure transformation temperatures under stress-free conditions. This testing method is well established, and tests are run under the applicable standard, ASTM F2004-17: Standard Test Method for Transformation Temperature of Nickel-Titanium Alloys by Thermal Analysis. Two other test methods for measuring strains and transformation temperatures under constant load or free recovery after prestraining have only recently been standardized—ASTM E3097: Standard Test Method for Mechanical Uniaxial Constant Force Thermal Cycling of SMAs (UCFTC) and ASTM E3098: Standard Test Method for Mechanical Uniaxial Pre-Strain and Thermal Free Recovery of SMAs (UPFR). These standards represent a critical step forward in producing reliable material property data for the use of these alloys in aeronautics and other commercial areas. However, no standard programs or software packages were previously available for postprocessing UCFTC- and UPFR-type test data to extract property data. Each organization that performed the testing analyzed data using its own custom manual methods, such as using a plot and a straight edge, spreadsheet plotting methods, or custom code routines, to extract the required values for strains, stresses, and transformation temperatures. SMAnalytics represents the first publicly available uniform software package for processing data generated using the DSC, UCFTC, and UPFR test methods, as well as many modifications of these methods, including loading in martensite versus austenite and performing multiple thermal cycles at stress. In doing so, it provides a tool for reducing potential error or variability in the measured values due to the precision of the technique used and person-to-person variability. It is also expected that this automated data-parsing tool can accelerate the data analysis phase of the test campaign, especially for large data files. This User’s Manual describes how the SMAnalytics software works and the method for its use.

Shape Memory Alloy↗
NASA NTRS2024

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

W. Dean Pesnell↗
NASA NTRS1994

Analysis of the Effects of Surface Pitting and Wear on the Vibrations of a Gear Transmission System

A comprehensive procedure to simulate and analyze the vibrations in a gear transmission system with surface pitting, 'wear' and partial tooth fracture of the gear teeth is presented. An analytical model was developed where the effects of surface pitting and wear of the gear tooth were simulated by phase and magnitude changes in the gear mesh stiffness. Changes in the gear mesh stiffness were incorporated into each gear-shaft model during the global dynamic simulation of the system. The overall dynamics of the system were evaluated by solving for the transient dynamics of each shaft system simultaneously with the vibration of the gearbox structure. In order to reduce the number of degrees-of-freedom in the system, a modal synthesis procedure was used in the global transient dynamic analysis of the overall transmission system. An FFT procedure was used to transform the averaged time signal into the frequency domain for signature analysis. In addition, the Wigner-Ville distribution was also introduced to examine the gear vibration in the joint time frequency domain for vibration pattern recognition. Experimental results obtained from a gear fatigue test rig at NASA Lewis Research Center were used to evaluate the analytical model.

Choy, F. K.↗
NASA NTRS2011

Compact Polarimetry in a Low Frequency Spaceborne Context

Compact polarimetry has been shown to be an interesting alternative mode to full polarimetry when global coverage and revisit time are key issues. It consists on transmitting a single polarization, while receiving on two. Several critical points have been identified, one being the Faraday rotation (FR) correction and the other the calibration. When a low frequency electromagnetic wave travels through the ionosphere, it undergoes a rotation of the polarization plane about the radar line of sight for a linearly polarized wave, and a simple phase shift for a circularly polarized wave. In a low frequency radar, the only possible choice of the transmit polarization is the circular one, in order to guaranty that the scattering element on the ground is illuminated with a constant polarization independently of the ionosphere state. This will allow meaningful time series analysis, interferometry as long as the Faraday rotation effect is corrected for the return path. In full-polarimetric (FP) mode, two techniques allow to estimate the FR: Freeman method using linearly polarized data, and Bickel and Bates theory based on the transformation of the measured scattering matrix to a circular basis. In CP mode, an alternate procedure is presented which relies on the bare surface scattering properties. These bare surfaces are selected by the conformity coefficient, invariant with FR. This coefficient is compared to other published classifications to show its potential in distinguishing three different scattering types: surface, doublebounce and volume. The performances of the bare surfaces selection and FR estimation are evaluated on PALSAR and airborne data. Once the bare surfaces are selected and Faraday angle estimated over them, the correction can be applied over the whole scene. The algorithm is compared with both FP techniques. In the last part of the paper, the calibration of a CP system from the point of view of classical matrix transformation methods in polarimetry is proposed.

radar polarization diversity↗
NASA NTRS2015

Calcium-magnesium Aluminosilicate (CMAS) Interactions with Advanced Environmental Barrier Coating Material

Particulates, like sand and volcanic ash, threaten the development of robust environmental barrier coatings (EBCs) that protect next-generation silicon-based ceramic matrix composite (CMC) turbine engine components from harsh combustion environments during service. The siliceous particulates transform into molten glassy deposits of calcium-magnesium aluminosilicate (CMAS) when ingested by an aircraft engine operating at temperatures above 1200C. In this study, a sample of desert sand was melted into CMAS glass to evaluate high-temperature interactions between the sand glass and an advanced EBC material. Desert sand glass was added to the surface of hot-pressed EBC substrates, which were then heated in air at temperatures ranging from 1200C to 1500C. Scanning electron microscopy and X-ray energy-dispersive spectroscopy were used to evaluate microstructure and phase compositions of specimens and the CMASEBC interface after heat treatments.

CMAS-coating interactions↗
NASA NTRS2012

Validation of Atmosphere/Ionosphere Signals Associated with Major Earthquakes by Multi-Instrument Space-Borne and Ground Observations

The latest catastrophic earthquake in Japan (March 2011) has renewed interest in the important question of the existence of pre-earthquake anomalous signals related to strong earthquakes. Recent studies have shown that there were precursory atmospheric/ionospheric signals observed in space associated with major earthquakes. The critical question, still widely debated in the scientific community, is whether such ionospheric/atmospheric signals systematically precede large earthquakes. To address this problem we have started to investigate anomalous ionospheric / atmospheric signals occurring prior to large earthquakes. We are studying the Earth's atmospheric electromagnetic environment by developing a multisensor model for monitoring the signals related to active tectonic faulting and earthquake processes. The integrated satellite and terrestrial framework (ISTF) is our method for validation and is based on a joint analysis of several physical and environmental parameters (thermal infrared radiation, electron concentration in the ionosphere, lineament analysis, radon/ion activities, air temperature and seismicity) that were found to be associated with earthquakes. A physical link between these parameters and earthquake processes has been provided by the recent version of Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) model. Our experimental measurements have supported the new theoretical estimates of LAIC hypothesis for an increase in the surface latent heat flux, integrated variability of outgoing long wave radiation (OLR) and anomalous variations of the total electron content (TEC) registered over the epicenters. Some of the major earthquakes are accompanied by an intensification of gas migration to the surface, thermodynamic and hydrodynamic processes of transformation of latent heat into thermal energy and with vertical transport of charged aerosols in the lower atmosphere. These processes lead to the generation of external electric currents in specific regions of the atmosphere and the modifications, by dc electric fields, in the ionosphere-atmosphere electric circuit. We retrospectively analyzed temporal and spatial variations of four different physical parameters (gas/radon counting rate, lineaments change, long-wave radiation transitions and ionospheric electron density/plasma variations) characterizing the state of the lithosphere/atmosphere coupling several days before the onset of the earthquakes. Validation processes consist in two phases: A. Case studies for seven recent major earthquakes: Japan (M9.0, 2011), China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and, Chile (M8.8, 2010) and B. A continuous retrospective analysis was preformed over two different regions with high seismicity- Taiwan and Japan for 2003-2009. Satellite, ground surface, and troposphere data were obtained from Terra/ASTER, Aqua/AIRS, POES and ionospheric variations from DEMETER and COSMIC-I data. Radon and GPS/TEC were obtaining from monitoring sites in Taiwan, Japan and Italy and from global ionosphere maps (GIM) respectively. Our analysis of ground and satellite data during the occurrence of 7 global earthquakes has shown the presence of anomalies in the atmosphere. Our results for Tohoku M9.0 earthquake show that on March 7th, 2011 (4 days before the main shock and 1 day before the M7.2 foreshock of March 8, 2011) a rapid increase of emitted infrared radiation was observed by the satellite data and an anomaly was developed near the epicenter. The GPS/TEC data indicate an increase and variation in electron density reaching a maximum value on March 8. From March 3 to 11 a large increase in electron concentration was recorded at all four Japanese ground-based ionosondes, which returned to normal after the main earthquake. Similar approach for analyzing atmospheric and ionospheric parameters has been applied for China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and Chile (M8.8, 2010) eahquakes. Results have revealed the presence of related variations of these parameters implying their connection with the earthquake process. The second phase (B) of this validation included 102 major earthquakes (M>5.9) in Taiwan and Japan. We have found anomalous behavior before all of these events with no false negatives. False alarm ratio for false positives is less then 10% and has been calculated for the same month of the earthquake occurrence for the entire period of analysis (2003-2009). The commonalities for detecting atmospheric/ionospheric anomalies are: i.) Regularly appearance over regions of maximum stress (i.e., along plate boundaries); ii.) Anomaly existence over land and sea; and iii) association with M>5.9 earthquakes not deeper than 100km. Due to their long duration over the same region these anomalies are not consistent with a meteorological origin. Our initial results from the ISTF validation of multi-instrument space-borne and ground observations show a systematic appearance of atmospheric anomalies near the epicentral area, one to seven (average) days prior to the largest earthquakes, and suggest that it could be explained by a coupling process between the observed physical parameters and the pre-earthquake preparation processes.

Ouzounov, Dimitar↗
NASA NTRS1992

Sulfur transformations in the sediments of a New Hampshire salt marsh

Summer sulfate reduction and sulfide and iron chemistry were monitored in marsh soils along a gradient from a creekside Spartina alterniflora region to an inland area dominated by S. patens. Sulfate reduction rates measured using S-35 increased from 0.4 in June to as much as 4.5 micro-mole/ml(sup -1)d(sup -1) in July in S. alterniflora soils with most rapid rates occurring in the upper few cm. Rates in S. patens soils were approximately equal to 5-8 fold slower with the most rapid rates occurring generally in soils deeper than 10 cm. The recovery percentage of reduced S-35 sulfur varied with depths at both locations; dissolved and acid-volatile sulfides dominating S. alterniflora regions while chromium-reducible solid phases were abundant in S. patens soils. Dissolved sulfide in S. alterniflora soils increased throughout the summer to approximately equal to 2.8 mM while sulfide in S. patens soils was abundant only in soils deeper than 15 cm. Dissolved sulfide covaried inversely with iron. Diel studies demonstrated that sulfide and iron varied approximately equal to two-fold in response to a semi-diurnal tide. Dissolved sulfide turnover was most rapid during periods of active plant growth.

Hines, Mark E.↗
NASA NTRS1995

Annual and Semi-Annual Temperature Oscillations in the Upper Mesosphere

Fourier transform spectrometer observations of the mesosphere have been performed at the University of Michigan (latitude: 42.5 N) on a long term basis. A database of near infrared Meinel hydroxyl spectra has been accumulated from which rotational temperatures have been determined. Harmonic analysis of one-day averaged temperatures for the period 1992.0 to 1994.5 has shown a distinct annual and semi-annual variation. Subsequent fitting of a five term periodic function characterizing the annual and semi-annual temperature oscillations to the daily averaged temperatures was performed. The resultant mean temperature and the amplitudes and phases of the annual and semi-annual variations are shown to coincide with an emission height slightly above 85 km which is consistent with the mean rocket derived altitude for peak nocturnal hydroxyl emission.

Niciejewski, R. J.↗
NASA NTRS2003

Chemistry and Evolution of Interstellar Clouds

In this chapter we describe how elements have been and are still being formed in the galaxy and how they are transformed into the reservoir of materials present at the time of formation of our protosolar nebula. We discuss the global cycle of matter, beginning at its formation site in stars, where it is ejected through winds and explosions into the diffuse interstellar medium. In the next stage of the global cycle occurs in cold, dense molecular clouds, where the complexity of molecules and ices increases relative to the diffuse ISM.. When a protostar forms in a dense core within a molecular cloud, it heats the surrounding infalling matter warms and releases molecules from the solid phase into the gas phase in a warm, dense core, sponsoring a rich gas-phase chemistry. Some material from the cold and warm regions within molecular clouds probably survives as interstellar matter in the protostellar disk. For the diffuse ISM, for cold, dense clouds, and for dense-warm cores, the physio-chemical processes that occur within the gas and solid phases are discussed in detail.

Wooden, D. H.↗
NASA NTRS1992

Wavefront sensing, control, and pointing

A majority of future NASA astrophysics missions from orbiting interferometers to 16-m telescopes on the Moon have, as a common requirement, the need to bring light from a large entrance aperture to the focal plane in a way that preserves the spatial coherence properties of the starlight. Only by preserving the phase of the incoming wavefront, can many scientific observations be made, observations that range from measuring the red shift of quasi-stellar objects (QSO's) to detecting the IR emission of a planet in orbit around another star. New technologies for wavefront sensing, control, and pointing hold the key to advancing our observatories of the future from those already launched or currently under development. As the size of the optical system increases, either to increase the sensitivity or angular resolution of the instrument, traditional technologies for maintaining optical wavefront accuracy become prohibitively expensive or completely impractical. For space-based instruments, the low mass requirement and the large temperature excursions further challenge existing technologies. The Hubble Space Telescope (HST) is probably the last large space telescope to rely on passive means to keep its primary optics stable and the optical system aligned. One needs only look to the significant developments in wavefront sensing, control, and pointing that have occurred over the past several years to appreciate the potential of this technology for transforming the capability of future space observatories. Future developments in space-borne telescopes will be based in part on developments in ground-based systems. Telescopes with rigid primary mirrors much larger than 5 m in diameter are impractical because of gravity loading. New technologies are now being introduced, such as active optics, that address the scale problem and that allow very large telescopes to be built. One approach is a segmented design such as that being pioneered by the W.M. Keck telescope now under construction at the Mauna Kea Observatory. It consists of 36 hexagonal mirror segments, supported on a framework structure, which are positioned by actuators located between the structure and the mirrors. The figure of the telescope is initialized by making observations of a bright star using a Shack Hartmann sensor integrated with a white light interferometer. Then, using sensed data from the mirror edges to control these actuators, the figure of the mosaic of 36 segments is maintained as if it were a rigid primary mirror. Another active optics approach is the use of a thin meniscus mirror with actuators. This technique was demonstrated on the European Southern Observatory's New Technology Telescope (NTT) and is planned for use in the Very Large Telescope (consists of four 8-m apertures), which is now entering the design phase.

Pitts, Thomas↗
NASA NTRS1987

The use of a numerical filter to correct airborne temperature measurements for the effects of sensor lag

A numerical filter for transforming measured temperature signals into a close approximation of the actual temperature signal is described. The filter is derived by minimizing the mean-square error of the system, and assuming a knowledge of the characteristics of the sensing element and its housing. The equation representing the frequency-response function of the numerical filter is given. Input and output spectra for a filter applied to a case with negligible noise and a noise level of 1.5 percent of the total power in the input spectrum are analyzed, and the numerical weights for these two cases are calculated. Phase angle and gain for the entire system are examined. It is noted that the filter can enhance spectral components as high as 8 Hz with little phase and gain degradation over the bandwidth.

Ritter, John A.↗