Communication theory applied to antenna systems
Communication theory applied to antenna systems - Fourier analysis, linear circuit theory, and aperture theory
ANTENNA↗
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Quasi-periodic oscillations in short recurring bursts of magnetars SGR 1806–20 and SGR 1900+14 observed with RXTE
Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars are of particular interest due to their potential to open up a window into the neutron star interior via neutron star asteroseismology. However, only three giant flares have been observed. We therefore make use of the much larger data set of shorter, less energetic recurrent bursts. Here, we report on a search for QPOs in a large data set of bursts from the two most burst-active magnetars, SGR 1806-20 and SGR 1900+14, observed with Rossi X-ray Timing Explorer. We find a single detection in an averaged periodogram comprising 30 bursts from SGR 1806–20, with a frequency of 57 Hz and a width of 5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This QPO fits naturally within the framework of global magneto-elastic torsional oscillations employed to explain giant flare QPOs. Additionally, we uncover a limit on the applicability of Fourier analysis for light curves with low background count rates and strong variability on short timescales. In this regime, standard Fourier methodology and more sophisticated Fourier analyses fail in equal parts by yielding an unacceptably large number of false-positive detections. This problem is not straightforward to solve in the Fourier domain. Instead, we show how simulations of light curves can offer a viable solution for QPO searches in these light curves.
79 ASTRONOMY AND ASTROPHYSICS↗
An Investigation into the Potential Application of Wavelets to Modal Testing and Analysis
The analysis of transient data of the type found in vibrating mechanical systems has been greatly improved through the use of modern techniques such as Fourier analysis. This is especially true when considered in conjunction with the development of the so-called Fast Fourier Transform algorithm by Cooley and the tremendous strides in computational power of the last several decades. The usefulness of the discrete Fourier Transform is its ability to transform sampled data from the "time-domain" to the "frequency domain," thereby allowing the analyst to decompose a signal into its frequency content. More recent developments have led to the wavelet transform. The strength of wavelet analysis is its ability to maintain both time and frequency information, thus making it an attractive candidate for the analysis of non-stationary signals. This report is an overview of wavelet theory and the potential use of the wavelet transform as an alternative to Fourier analysis in modal identification.
A. Fort Gwinn, Jr.↗
A note on the ability to predict transonic drag-rise changes due to model modifications
Wind tunnel test to establish validity of Fourier analysis results for transonic drag rise changes due to model modifications
FOURIER ANALYSIS↗
A novel approach to characterizing the surface topography of niobium superconducting radio frequency (SRF) accelerator cavities
As superconducting niobium radio-frequency (SRF) cavities approach fundamental material limits, there is increased interest in understanding the details of topographical influences on realized performance limitations. Micro- and nano-roughness are implicated in both direct geometrical field enhancements as well as complications of the composition of the 50 nm surface layer in which the super-currents typically flow. Interior surface chemical treatments such as buffered chemical polishing (BCP) and electropolishing (EP) used to remove mechanical damage leave surface topography, including pits and protrusions of varying sharpness. These may promote RF magnetic field entry, locally quenching superconductivity, so as to degrade cavity performance. A more incisive analysis of surface topography than the widely used average roughness is needed. In this study, a power spectral density (PSD) approach based on Fourier analysis of surface topography data acquired by both stylus profilometry and atomic force microscopy (AFM) is introduced to distinguish the scale-dependent smoothing effects, resulting in a novel qualitative and quantitative description of Nb surface topography. The topographical evolution of the Nb surface as a function of different steps of well-controlled EP is discussed. This study will greatly help to identify optimum EP parameter sets for controlled and reproducible surface levelling of Nb for cavity production.
43 PARTICLE ACCELERATORS↗
Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions
This study describes the effect of hysteresis on the generation of the higher harmonics in the line voltage and current in a non-uniform transmission line when we include a quadratic non-linear term having memory to account for the hysteresis effect in the inductance part of line. The simulational analysis using MATLAB is presented which works with a non-uniform line having hysteresis. These simulations are based on a theoretical spatial Fourier analysis combined with perturbation theory which is used without bothering about source and load. The line differential equations are solved approximately in the space- time-frequency domain using perturbation theory and the numerical computations have been carried out for the voltage and current amplitude characteristics. In Appendix 1, some theoretical explanations that support our non-linear memory-based hysteresis model based on Landau’s equation of precession of a magnetic moment in a magnetic field are included. This paper also includes a brief derivation of atomic transition probability produced by e-m radiation from the transmission line falling on an atom in the far field zone. This calculation enables us to derive maximum likelihood estimation(MLE) of the hysteresis parameters by measuring which atomic transitions have occurred.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Flow transition with 2-D roughness elements in a 3-D channel
We develop a new numerical approach to study the spatially evolving instability of the streamwise dominant flow in the presence of roughness elements. The difficulty in handling the flow over the boundary surface with general geometry is removed by using a new conservative form of the governing equations and an analytical mapping. The numerical scheme uses second-order backward Euler in time, fourth-order central differences in all three spatial directions, and boundary-fitted staggered grids. A three-dimensional channel with multiple two-dimensional-type roughness elements is employed as the test case. Fourier analysis is used to decompose different Fourier modes of the disturbance. The results show that surface roughness leads to transition at lower Reynolds number than for smooth channels.
Liu, Zhining↗
DFT-based spectral moments estimators for spaceborne Doppler precipitation radar
In this paper an in-depth analysis on the performance of the Fourier analysis in estimating the first spectral moment of Doppler spectra of rain signals from a spaceborne radar is presented.
precipitation radar Doppler CAMEX-4↗
A Spectral-line Analysis of the G8 III Standard ε VIR
Eleven seasons of spectroscopic data comprised of 107 exposures for the stable G8 III standard star, ε Vir are analyzed for projected rotation rate and granulation parameters. A Fourier analysis of the line shapes yield v sin i = 3.06 ± 0.20 km s{sup −1} and a radial-tangential macroturbulence dispersion ζ {sub RT} = 5.16 ± 0.08 km s{sup −1}. The radial velocity over nine seasons is constant to 18 m s{sup −1}. The absolute radial velocity with granulation blueshifts (but not gravitational redshift) removed is −14120 ± 75 m s{sup −1}. Line-depth ratios show the temperature to be constant to 0.7 K over 11 years, although a small secular rise or cyclic variation ∼1 K cannot be ruled out. The third-signature plot shows that the star has granulation velocities 10% larger than the Sun's. Mapping the Fe i λ 6253 line bisector on to the third-signature plot indicates a normal-for-giants flux deficit area of 12.8%, indicating ∼134 K temperature difference between granules and lanes. Deficit velocities of GK giants are seen to shift to higher values with higher luminosity, ∼0.75 km s{sup −1} over Δ M {sub V} ∼ 1.5, indicating larger velocity differences between granules and lanes for giants higher in the HR diagram.
79 ASTRONOMY AND ASTROPHYSICS↗
KIC 12602250: A Low-amplitude Double-mode Delta Scuti Star with Amplitude Modulation
We report a detailed light-curve analysis of the Kepler target Kepler Input Catalog (KIC) 12602250. The results show that KIC 12602250 is a low-amplitude radial double-mode δ-Scuti star with amplitude modulation. The Fourier analysis of the long cadence data (i.e., Q0—Q17, spanning 1471 days) reveals that the variations of the light curve are dominated by the strongest mode with frequency F0 = 11.6141 d{sup -1}, suggesting that KIC 12602250 is a δ-Scuti star. The other independent mode F1 = 14.9741 d{sup -1} is newly detected. The amplitude of the light variations of KIC 12602250 is ~0.06 mag, which indicates that this is a low-amplitude δ-Scuti star; but the ratio of F0/F1 is estimated as 0.7756, which is typical of HADS, and a slow amplitude growth is detected in F1 and f {sub 3}, which could be due to stellar evolution, suggesting that KIC 12602250 could be a post-main-sequence δ Scuti that is crossing the instability strip for the first time.
79 ASTRONOMY AND ASTROPHYSICS↗
ON THE FOURIER AND WAVELET ANALYSIS OF CORONAL TIME SERIES
Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence and Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence and Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.
79 ASTRONOMY AND ASTROPHYSICS↗
A general theory of interference fringes in x-ray phase grating imaging
Purpose: The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. Methods: In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. Results: The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. Conclusions: In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A linear stability analysis for nonlinear, grey, thermal radiative transfer problems
We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Program for the analysis of time series
A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.
Brown, T. J.↗
CMFD and coarse-mesh DSA
The Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are two widely-used, independently-developed acceleration methods for iteratively solving deterministic particle transport simulations. In this paper we show that these methods are related in the following way: if the standard notion of DSA as a 'fine mesh' method is generalized to that of a coarse mesh method, then the linearized form of CMFD is algebraically equivalent to a coarse mesh form of DSA. Also, we demonstrate theoretically (via Fourier analysis) and computationally that CMFD and coarse mesh DSA have nearly the same convergence properties. (authors)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Effects of low frequency vibration of a limb
Low frequency oscillations were applied on the ankle joint in plantarflexion/dorsiflexion rotation using a torque motor. The torque, the angular rotation and the evoked electromyogram from the gastronemius soleus and the anterior tibial muscles were recorded. Significant nonlinearities were observed in the angular rotation from 8 to 12 Hz. The following methods are used for data analysis: (1) Two cycle averaged response; (2) Fourier transform; and (3) Fourier analysis at the driving frequency. Important observations are: (1) resonance near 6 to 8 Hz; (2) slowly increasing amplitudes of oscillation near resonance; (3) self sustaining oscillations after the motor is turned off, particularly in the fatigued limb; and (4) distortion of angular rotation during which there are spontaneous recurrences of oscillation at the driving frequency.
Agarwal, G. C.↗
TAKING ADVANTAGE OF THE COS TIME-TAG CAPABILITY: OBSERVATIONS OF PULSATING HOT DQ WHITE DWARFS AND DISCOVERY OF A NEW ONE
We present an analysis of the ultraviolet light curves of five Hot DQ white dwarfs recently observed with the Cosmic Origins Spectrograph (COS) on board the Hubble Space Telescope (HST). These light curves were constructed by extracting the time-tag information from the FUV and NUV spectroscopic data. Single-color light curves were thus produced in 60 s time bins. The Fourier analysis of these data successfully recovers the main pulsation modes of the three stars previously known to be variable from ground-based observations. We also report the discovery of pulsations in another object, SDSS J1153+0056, making it only the fifth member of the new class of variable Hot DQ stars and the first pulsating white dwarf to be discovered from space-based observations. The relatively high amplitudes of the modes observed in the FUV (2-4 times that observed in the optical) as well as the high fraction of stars variable in our sample suggest that most, if not all, Hot DQ white dwarfs might be pulsating at some level when observed at high enough sensitivity. Our results also underline the vast potential of the time-tag capability of the HST/COS combination.
79 ASTRONOMY AND ASTROPHYSICS↗
Nonoverlapping block smoothers for the Stokes equations
Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are nonoverlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, using multigrid methods to efficiently solve more difficult problems such as the Stokes equations leads to computationally more expensive smoothers, for example, overlapping block smoothers. Nonoverlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new nonoverlapping smoothers, the so-called triad-wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and nonoverlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.
97 MATHEMATICS AND COMPUTING↗