Fourier Transformation Of Data Research Articles

Spectroscopic data, spin-orbit functions, and revised analysis of strong perturbative interactions for theA 1Σ+andb 3Πstates of RbCs

The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the $A{ }^{1}{\ensuremath{\Sigma}}^{+}$-$b{ }^{3}\ensuremath{\Pi}$ complex. The $A$-$b$ mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed $A$-$b\ensuremath{\rightarrow}X$ transitions, while the second is derived in large part from $(4){ }^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}A$-$b$ emission and extends to higher $A$-$b$ energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the $A$ state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the $b$ state is established with a considerable degree of certainty with help of data on the $^{85}\mathrm{Rb}$$^{133}\mathrm{Cs}$ and $^{87}\mathrm{Rb}$$^{133}\mathrm{Cs}$ isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two ${\ensuremath{\Omega}}^{p}={0}^{+}$ states, $A{ }^{1}{\ensuremath{\Sigma}}^{+}$ and $b{ }^{3}{\ensuremath{\Pi}}_{0+}$, happens to agree rather well with the results from both of these methods, while for the diagonal $b{ }^{3}\ensuremath{\Pi}$ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.

Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method

The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.

Change in the surface properties of poly(vinylidene fluoride) films by treatment in direct-current discharge

It has been found that treatment in dc discharge results in a substantial and time-invariant increase in the surface energy of poly(vinylidene fluoride) films. This effect is obviously due to the formation of oxygen-containing groups on the polymer surface, a fact that is corroborated by Fourier-transform IR spectroscopy and X-ray photoelectron spectroscopy data. It has been shown that dc discharge is more effective in altering the contact properties of the polymer surface than low-frequency glow discharge.

Mass Measurement Errors of Fourier-Transform Mass Spectrometry (FTMS): Distribution, Recalibration, and Application

The hybrid linear trap quadrupole Fourier-transform (LTQ-FT) ion cyclotron resonance mass spectrometer, an instrument with high accuracy and resolution, is widely used in the identification and quantification of peptides and proteins. However, time-dependent errors in the system may lead to deterioration of the accuracy of these instruments, negatively influencing the determination of the mass error tolerance (MET) in database searches. Here, a comprehensive discussion of LTQ/FT precursor ion mass error is provided. On the basis of an investigation of the mass error distribution, we propose an improved recalibration formula and introduce a new tool, FTDR (Fourier-transform data recalibration), that employs a graphic user interface (GUI) for automatic calibration. It was found that the calibration could adjust the mass error distribution to more closely approximate a normal distribution and reduce the standard deviation (SD). Consequently, we present a new strategy, LDSF (Large MET database search and small MET filtration), for database search MET specification and validation of database search results. As the name implies, a large-MET database search is conducted and the search results are then filtered using the statistical MET estimated from high-confidence results. By applying this strategy to a standard protein data set and a complex data set, we demonstrate the LDSF can significantly improve the sensitivity of the result validation procedure.

Noise Attributes of LWIR HDVIP HgCdTe Detectors

Time series and Fourier-transform data on high-density vertically integrated photodiodes (HDVIP) at 0 and 50 mV reverse bias in the dark have been studied. The detectors have a cutoff wavelength λc (60 K) of 10.5 μm. Examination of the detector current time series and Fourier-transform curves of these devices reveals a variety of interesting characteristics: (i) time series displaying switching between four states characteristic of random telegraph signal (RTS) noise, the noise current power spectrum having Lorentzian or double Lorentzian type characteristics, (ii) time series data exhibiting wave-like characteristics with the noise current power spectrum being 1/f2-like at low frequencies, (iii) time series having a mean value independent of time with the noise current power spectrum being white, and (iv) time series nearly independent of time with the noise current power spectrum having 1/f characteristics. Although from a single array, the excess noise characteristics at low (mHz) frequencies were varied, most of the detectors measured fell into one of these four categories. The predominance of detectors examined had minimal excess low-frequency noise down to ~ 10 mHz. Detectors that displayed RTS noise in reverse bias were repeatable under subsequent measurement. However, when measured at zero bias, the same detectors exhibited no RTS noise, the noise current power spectrum being white in nature.

Effects of zero-filling and apodization on spectral integrals in discrete Fourier-transform spectroscopy of noisy data

The influence of noise on the standard deviation of spectral integrals is examined. Calculations assuming discrete Fourier-transform data are compared with Monte-Carlo simulations. The effects of zero-filling and apodization are examined for free-induction-decay (FID) signals and for symmetric spin–echo signals in one and two dimensions, with particular attention to features not previously presented in the literature. Findings suggest that for mild apodization, the known sensitivity enhancement due to zero-filling in either the real or the imaginary part signal [E. Bartholdi, R.R. Ernst, Fourier spectroscopy and the causality principle, J. Magn. Reson., 11 (1973) 9–19] is maintained; however, for stronger apodization filters, this enhancement can be obliterated completely. It is shown that results obtained by analysis of one-dimensional signals can be readily applied to multi-dimensional data. Furthermore, zero-filling has a negligible effect for symmetric spin–echo signals with implications for signal averaging in magnetic resonance imaging and spectroscopic imaging.

Applying Fast Fourier Transform Analysis and Data Window in Software Global Positioning System Receivers to Mitigate Continuous Wave Interference under Dynamic Conditions

Traditionally, most Radio Frequency Interference mitigation methods have been implemented and tested using conventional hardware receivers. With the rapid development of computer technologies, the signal-processing computational load is becoming less of a concern, and thus it becomes feasible to develop and test new interference mitigation methods based on software receivers together with modern digital signal-processing techniques. This paper describes an investigation into the development of a narrow-band Continuous Wave (CW) interference mitigation algorithm and performance testing using a software Global Positioning System receiver based on Fast Fourier Transform analysis and data windowing. In this paper, some strategies were proposed to improve the anti-jamming performance. First, for high-level interference, a fixed detection threshold suggested in previous literature is not optimal. An adaptive detection threshold that is of better performance and is a function of the standard deviation of the normalized spectrum and the correlator power output was used in lieu. Second, a priori information-based soft thresholding techniques for both bit synchronization and enhanced signal acquisition were applied under high dynamic conditions and high-level interference environments. The factors that are crucial for weak-signal detection and tracking, namely, coherent integration time, tracking loop bandwidth, and integration time in the loop filter were evaluated to assess the effectiveness of this algorithm. Some interference suppression strategies for spread spectrum systems, namely, windowing and overlap processing, were also investigated. Test results proved that the proposed algorithm is effective to mitigate narrow-band CW interference under certain power level. Windowing and overlapped processing are good strategies to further improve the anti-interfernce capability by 2 dB.

Fourier Transform Emission Spectra of the (000)–(000) Band of the λ4051.6 Band of C3

The (000)–(000) band of the 4051.6 8 group ( ˜ A 1 � u ˜ X 1 � þ )o f C3 was recorded in emission with a Bruker IFS 120HR Fourier transform (FT) spectrometer at the University of Waterloo. The band was excited by a microwave discharge in isopropanol (less than a few mtorr) diluted in helium (2 torr). Our new FT data provide more reliable and accurately calibrated transition wavenumbers than those from the grating spectra given by Gausset and coworkers. Analysis of our new spectrum combined with the data by McCall and coworkers confirmed that the lower J levels in the ˜ A state were strongly perturbed, as reported by Gausset and coworkers. The unidentified lines observed by McCall and coworkers could be attributed to extra transitions to an unknown perturbing state. Subject heading gs: astrochemistry — ISM: clouds — ISM: molecules — methods: laboratory — molecular data

Spectral response from modulus time domain data of disordered materials

The electric response of the glass-forming glycerol and crystalline ionic conductor Li0.18La0.61TiO3 is probed by modulus time domain measurements. A capacity correction algorithm is proposed to overcome the low capacitance limit of the technique. This method allows to Fourier-transform time domain data yielding undisturbed permittivity spectra. The algorithm is checked first in glycerol, where the dielectric data recorded in frequency and time domain show an overlap of several decades. It is also applied to match the dielectric data of the crystalline ionic conductor Li0.18La0.61TiO3 from modulus time domain with overlapping frequency domain data, forming data sets covering 11 decades in frequency. The extension of the electrical characterization to low frequencies allows the detection of an Arrhenius behavior for the dc ionic conductivity at low temperatures, in disagreement with previous analysis in terms of Vogel-Fulcher-Tammann laws.

고속 전철용 가선-팬터그래프 시스템의 모델링 및 접촉력 해석

In this study, the dynamic characteristics of a catenary system and pantograph supplying electrical power to high-speed trains are investigated. One of the most important issues accompanied by increasing the speed of high-speed rail is stabilization of current collection. To stabilize current collection, it is necessary the contact force between the catenary and the pantograph to be kept continuous without loss of contact. The analytical model of a catenary and a pantograph is constructed to simulate the behavior of an actual system. The analysis of the catenary based on the Finite Element Method (FEM) is performed to develop a catenary model suitable for high speed operation. The reliability of the models is verified by the comparison of the excitation test with Fast Fourier Transform (FFT) data of the actual system. The static deflection of the catenary, stiffness variation in contact lines, dynamic response of the catenary undergoing constant moving load, contact force, and each state of the pantograph model were calculated. It is confirmed that a catenary and pantograph model are necessary for studying the dynamic behavior of the pantograph system.

Analysis of strongly coupled electronic states in diatomic molecules: Low-lying excited states of RbCs

Analysis and assignment of spectra involving the lowest excited states of the heavier alkali-metal atom dimers are complicated by the strong spin-orbit coupling elements. Here we report an analysis of the Fourier-transform spectroscopy data from laser-induced fluorescence of the coupled $A{}^{1}{\ensuremath{\Sigma}}^{+}$ and $b{}^{3}\ensuremath{\Pi}$ states of RbCs, using the discrete variable representation. Fitted parameters are given and special effects due to strong coupling are discussed.

Rotational Analysis of the ν6 Band in Furan (C4H4O)

Abstract We recorded and analyzed the absorption spectrum of the ν 7 fundamental band in furan, observed around 995 cm −1 . Fourier transform (FT) spectroscopy was used at ULB to record the spectrum under room-temperature conditions, at 0.01 cm −1 instrumental resolution. Diode–laser (DL) spectroscopy in a supersonic jet was used to record some portions of the band at Lille, revealing the fine structure around the band center. Pure rotation (MMW) data in the upper state were also recorded at Lille. Some 5559 FT, 101 DL, and 23 MMW data were assigned in this work. We fitted, on one hand, the MMW and DL data together and, on the other hand, the MMW, DL, and FT data simultaneously using a weighted procedure, constraining the ground state constants to their value determined from the microwave data in the literature. The results from these fits are provided and the constants discussed. Ab initio calculations are also performed to provide a force field which is used to support the very strong increase with the vibrational excitation observed in the inertial defect determined from the experimental rotational constants.

Correlation of the Raman spectra with the thermal conductivity of a set of diamond wafers prepared by chemical vapor deposition

Raman spectroscopy, at laser excitation wavelengths of 514.5, 785, and 1064 nm, is used to study a set of chemical-vapor-deposited (CVD) diamond wafers of known thermal conductivity κ. The in-plane thermal conductivity (at 25 °C) of the diamond wafers ranges from 4 to 22 W cm−1 K−1 and represents a wide range of diamond quality. The spectra were obtained from both macro/micro- sampling measurements, examining the top and bottom wafer surface, as well as wafer cross-sections. Discussed are the peak positions and linewidths of the Raman bands and their relation to sp3-bonded diamond and sp2-bonded carbon in the context of diamond quality and perfection, and the effects of wafer heterogeneities. The detailed analysis of the Raman spectra provides a robust correlation with the room-temperature bulk (or macroscopic) thermal conductivity of these samples. The correlation is made through the determination of the band area ratios of the diamond Raman line at 1333 cm−1 to that of the 1550 cm−1 band characteristic of nondiamond carbon impurities. This dependence is most pronounced for the Fourier-transform Raman data obtained with infrared excitation at 1064 nm, due to resonance enhancement, and therefore allows the detection of carbon impurities, especially for high-quality CVD diamond.

Investigation of 13CH3OH methanol: new laser lines and assignments

We have reinvestigated 13 CH 3 OH as a source of far-infrared (FIR) laser emission using a CO 2 laser as a pumping source. Thirty new FIR laser lines in the range 36.5 μm to 202.6 μm were observed and characterized. Five of them have wavelengths between 36.5 and 75 μm and have sufficient intensity to be used in LMR spectroscopy. Using Fourier-transform spectroscopic data in the infrared (IR) and FIR regions we have determined the assignment for 10 FIR laser transitions and predict nine frequencies for laser lines which have yet to be observed.

Rotational Analysis of the ν7 Band in Furan (C4H4O)

We recorded and analyzed the absorption spectrum of the ν7 fundamental band in furan, observed around 995 cm−1. Fourier transform (FT) spectroscopy was used at ULB to record the spectrum under room-temperature conditions, at 0.01 cm−1 instrumental resolution. Diode–laser (DL) spectroscopy in a supersonic jet was used to record some portions of the band at Lille, revealing the fine structure around the band center. Pure rotation (MMW) data in the upper state were also recorded at Lille. Some 5559 FT, 101 DL, and 23 MMW data were assigned in this work. We fitted, on one hand, the MMW and DL data together and, on the other hand, the MMW, DL, and FT data simultaneously using a weighted procedure, constraining the ground state constants to their value determined from the microwave data in the literature. The results from these fits are provided and the constants discussed. Ab initio calculations are also performed to provide a force field which is used to support the very strong increase with the vibrational excitation observed in the inertial defect determined from the experimental rotational constants.

Role of support information and zero locations in phase retrieval by a quadratic approach

A recently introduced approach to phase-retrieval problems is applied to present a unified discussion of support information and zero locations in the reconstruction of a discrete complex image from Fourier-transform phaseless data. The choice of the square-modulus function of the Fourier transform of the unknown as the problem datum results in a quadratic operator that has to be inverted, i.e., a simple nonlinearity. This circumstance makes it possible to consider and to point out some relevant factors that affect the local minima problem that arises in the solution procedure (which amounts to minimizing a quartic functional). Simple modifications of the basic procedure help to explain the role of support information and zeros in the data and to develop suitable strategies for avoiding the local minima problem. All results can be summarized by reference to the ratio between the effective dimensions of the data space and the space of unknowns. Numerical results identify the approach’s considerable robustness against false solutions, starting from completely random first guesses, if the above ratio is larger than 3. The algorithm also ensures robust performance in the presence of noise in the data.

Image reconstruction from pairs of Fourier-transform magnitude

The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms.

Nuclear magnetic resonance: concepts and methods

Structure of Nuclear Magnetic Resonance Spectra. Basic Mathematics and Physics of NMR. Fourier Transform NMR and Data Processing. Dynamic Phenomena in NMR. Multipulse and Multidimensional NMR. Index.

Fast-ion beam laser spectroscopy of 14N2+ and 15N2+: high-resolution study of the (1, 2) band of the B2Σu+X2Σg+ system

Abstract We used laser-induced fluorescence combined with fast-ion beam laser spectroscopy to study at high resolution the rotational structure of the (1, 2) band of the first negative system (B2Σu+X2Σg+ of 14N2+ and 15N2+. Combining our laser-induced fluorescence data for the BX band and the new Fourier-transform emission data for the Meinel A-X system, we removed the correlation between the X and B state and we determined more accurate values of the molecular parameters for the excited and perturbed states of 14N2+ and 15N2+. The vibrational level v′ = 1 of the B state was found to be unperturbed within the observed rotational levels (4 A 2 Π u state.

Multiple-Window Spectrum Estimation Applied toin VivoNMR Spectroscopy

Multiple-window spectrum estimation (MWSE) is a method of deriving frequency spectra from time series. A set of apodizing windows is applied to the time data and each windowed data set is Fourier transformed. The windows are prolate spheroidal sequences. These form the orthonormal set of functions that is maximally concentrated in both time and frequency domains. An iterative algorithm is then applied to the data set to find a least-squares estimate of the power spectrum. In addition, statistical tests may be applied to determine the existence of periodic components at particular frequencies, their amplitudes, phases, and positions. The method is quantitative and makes no lineshape assumptions. Computer simulations were used to compare MWSE performance with that of conventional Fourier-transform processing with quantification by curve fitting. Signal-to-noise ratio, spectral resolution, linearity, and susceptibility to artifacts were compared. MWSE gives similar signal-to-noise ratio and spectral resolution to Fourier-transform data and is linear over three orders of magnitude but is much more robust with respect to artifacts. In particular, data truncation introduces no baseline distortion, broad baseline humps are removed automatically, and large solvent peaks may be easily removed without affecting adjacent lines. No separate phase correction is required. MWSE gives more accurate quantitative spectra, particularly when the time data are imperfect. The method is, therefore, particularly appropriate for processingin vivodata. The utility of the MWSE method is demonstrated onin vivo1H,31P, and13C NMR spectroscopy data.