Construction and Fourier Analysis of Invariant Surfaces from Tracking Data
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Warnock, R.↗
SEARCH · Engineering Papers
Results for “Fourier analysis”
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Measurement of Multibunch Transfer Functions Using Time Domain Data and Fourier Analysis
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Fox, J.↗
Sampling Time Errors in Discrete Fourier Analysis
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Horelick, D.↗
Fourier analysis by spectral transformation (Fast) Photonic Doppler Velocimetry (PDV) with signal fade mitigation
A state-of-the-art class of photonic Doppler velocimetry (PDV) diagnostic and novel methods to stabilize any class of PDV signal has been developed. The former brings velocimetry to new extremes in maximum velocity and fast time resolution, while maintaining precision velocity resolution, long record length capability, and the ability to record multiple velocities simultaneously. The latter compensates for large changes in signal intensity common in many experiments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Influence of the earth's magnetic field on the diurnal variation of foF2 /Fourier analysis/
Fourier analysis of diurnal variations in F- 2 ionospheric layer induced by earth magnetic field
MAGNETIC FIELD↗
A Critical Examination of Wind-Wave Spectral Functional Form
Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.
Huang, Norden E.↗
Structures of aspartic acid-96 in the L and N intermediates of bacteriorhodopsin: analysis by Fourier transform infrared spectroscopy
The light-induced difference Fourier transform infrared spectrum between the L or N intermediate minus light-adapted bacteriorhodopsin (BR) was measured in order to examine the protonated states and the changes in the interactions of carboxylic acids of Asp-96 and Asp-115 in these intermediates. Vibrational bands due to the protonated and unprotonated carboxylic acid were identified by isotope shift and band depletion upon substitution of Asp-96 or -115 by asparagine. While the signal due to the deprotonation of Asp-96 was clearly observed in the N intermediate, this residue remained protonated in L. Asp-115 was partially deprotonated in L. The C = O stretching vibration of protonated Asp-96 of L showed almost no shift upon 2H2O substitution, in contrast to the corresponding band of Asp-96 or Asp-115 of BR, which shifted by 9-12 cm-1 under the same conditions. In the model system of acetic acid in organic solvents, such an absence of the shift of the C = O stretching vibration of the protonated carboxylic acid upon 2H2O substitution was seen only when the O-H of acetic acid is hydrogen-bonded. The non-hydrogen-bonded monomer showed the 2H2O-dependent shift. Thus, the O-H bond of Asp-96 enters into hydrogen bonding upon conversion of BR to L. Its increased hydrogen bonding in L is consistent with the observed downshift of the O-H stretching vibration of the carboxylic acid of Asp-96.
NASA Discipline Exobiology↗
Fourier functional analysis for unsteady aerodynamic modeling
A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.
Lan, C. Edward↗
Fourier functional analysis for unsteady aerodynamic modeling
A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.
Chin, Suei↗
Synthesis and characterization of Ni(II) complex with 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradeca-7,14-dienium bromide
Nickel(II) complex have been synthesized by treating a 14-membered ring tetraaza macrocyclic compound, 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradeca-7,14-dienium, bromide (Me{sub 6}N{sub 4}H{sub 4})Br{sub 2} with nickel acetate in metanol. The complex was characterized using elemental analysis, Fourier Transform Infrared (FTIR), Ultraviolet-Visible (UV-Vis), and single crystal diffraction (X-ray). The nickel atom coordinates through four nitrogen atoms in the ligand. Square planar geometry has been proposed for this complex.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
0.94-2.42 μm ground-based transmission spectra of the hot Jupiter HD-189733b
We present here new transmission spectra of the hot Jupiter HD-189733b using the SpeX instrument on the NASA Infrared Telescope Facility. We obtained two nights of observations where we recorded the primary transit of the planet in the J, H, and K bands simultaneously, covering a spectral range from 0.94 to 2.42 μm. We used Fourier analysis and other detrending techniques validated previously on other data sets to clean the data. We tested the statistical significance of our results by calculating the autocorrelation function, and we found that, after the detrending, autocorrelative noise is diminished at most frequencies. Additionally, we repeated our analysis on the out-of-transit data only, showing that the residual telluric contamination is well within the error bars. While these techniques are very efficient when multiple nights of observations are combined together, our results prove that even one good night of observations is enough to provide statistically meaningful data. Our observed spectra are consistent with space-based data recorded in the same wavelength interval by multiple instruments, indicating that ground-based facilities are becoming a viable and complementary option to spaceborne observatories. The best fit to the features in our data was obtained with water vapor. Our error bars are not small enough to address the presence of additional molecules; however, by combining the information contained in other data sets with our results, it is possible to explain all the available observations with a modeled atmospheric spectrum containing water vapor, methane, carbon monoxide, and hazes/clouds.
79 ASTRONOMY AND ASTROPHYSICS↗
Fast Fourier transform analysis of rotor-bearing systems
Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.
Choy, K. C.↗
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
SantaMaria, Odilyn L.↗
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
SantaMaria, Odilyn L.↗
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
SantaMaria, Odilyn L.↗
Minimal Joule dissipation models of magnetospheric convection
This paper gives a topical review of theoretical models of magnetospheric convection based on the concept of minimal Joule dissipation. A two-dimensional slab model of the ionosphere featuring an enhanced conductivity auroral oval is used to compute high-latitude electric fields and currents. Mathematical methods used in the modeling include Fourier analysis, fast Fourier transforms, and variational calculus. Also, conformal transformations are introduced in the analysis, which enable the auroral oval to be represented as a nonconcentric, crescent-shaped figure. Convection patterns appropriate to geomagnetic quiet and disturbed conditions are computed, the differentiating variable being the relative amount of power dissipated in the magnetospheric ring current. When ring current dissipation is small, the convection electric field is restricted to high latitudes (shielding regime), and when it is large, a significant penetration of the field to low latitudes occurs, accompanied by an increase in the ratio of the region I current to the region 2 current.
Barbosa, D. D.↗
Broadband turbulent spectra in gamma-ray burst light curves
Broadband power density spectra offer a window to understanding turbulent behavior in the emission mechanism and, at the highest frequencies, in the putative inner engines powering long gamma-ray bursts (GRBs). We describe a chirp search method alongside Fourier analysis for signal detection in the Poisson noise-dominated, 2 kHz sampled, BeppoSAX light curves. An efficient numerical implementation is described in O(Nnlog n) operations, where N is the number of chirp templates and n is the length of the light-curve time series, suited for embarrassingly parallel processing. For the detection of individual chirps over a 1 s duration, the method is one order of magnitude more sensitive in signal-to-noise ratio than Fourier analysis. The Fourier-chirp spectra of GRB 010408 and GRB 970816 show a continuation of the spectral slope with up to 1 kHz of turbulence identified in low-frequency Fourier analysis. The same continuation is observed in an average spectrum of 42 bright, long GRBs. An outlook on a similar analysis of upcoming gravitational wave data is included.
79 ASTRONOMY AND ASTROPHYSICS↗
Interferogram analysis using Fourier transform techniques
A method of interferogram analysis is described in which Fourier transform techniques are used to map the complex fringe visibility in several types of interferograms. Algorithms are developed for estimation of both the amplitude and the phase of the fringes (yielding the modulus and the phase of the holographically recorded object Fourier transform). The algorithms were applied to the reduction of interferometric seeing measurements (i.e., the estimation of the fringe amplitude only), and the reduction of interferometric tests (i.e., estimation of the fringe phase only). The method was used to analyze scatter-plate interferograms obtained at NOAO.
Roddier, Claude↗