scholarly journals Fourier Analysis of Line-Profile Variations: Toward Stellar m – v Diagrams?

1993 ◽  
Vol 139 ◽  
pp. 148-148
Author(s):  
W.J. Merryfield ◽  
E.J. Kennelly
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Power Spectrum ◽  
Spectral Line ◽  
Single Mode ◽  
Two Dimensional ◽  
Line Profiles ◽  
Azimuthal Position ◽  
Scuti Stars ◽  
Straightforward Interpretation

AbstractNumerous rapidly rotating δ Scuti stars exhibit variable line profiles containing traveling subfeatures [l]-[2], which may be signatures of nonradial pulsations having relatively high azimuthal order |m| We describe a procedure whereby a time series of spectral line profiles is Fourier analysed both in time and in a wavelength variable that is presumed to correspond to azimuthal position Φ on the star. What such an analysis can tell us is examined by analysing artificially-generated data. For an ideal example in which sin i = 1 and a single mode having is present, the two-dimensional Fourier transform yields a power spectrum in frequency and an apparent azimuthal order that provides a good indication of the actual and m. Such a straightforward interpretation is also possible when sin i < 1, and when multiple sectoral modes are present. For tesseral modes may correspond more closely to than to m.

scholarly journals Mode Determination by Fourier Analysis of Line-Profile Variations: Application to τ Peg

1993 ◽  
Vol 139 ◽  
pp. 147-147
Author(s):  
E.J. Kennelly ◽  
G.A.H. Walker ◽  
W.J. Merryfield ◽  
J.M. Matthews
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Line Profiles ◽  
High Resolution Data ◽  
Low Degree ◽  
Scuti Star ◽  
High Degree ◽  
Scuti Stars ◽  
Resolution Data ◽  
Good Agreement

AbstractThe identification of modes of oscillation is an important first step towards the seismology of stars. Low- and high-degree nonradial modes of oscillation may appear as variations in the line profiles of rapidly rotating δ Scuti stars. We present a technique whereby complex patterns in the line profiles are decomposed into Fourier components in both time and “Doppler space”. The technique is applied to the 7.3-hour time series of high-resolution data obtained from CFHT for the δ Scuti star τ Peg. In addition to the low-degree mode which has been identified in photometric studies (Breger 1991), we find evidence for at least three high-degree modes near 11 and 15. Correcting for the rotation of the star, most of these modes appear to oscillate with frequencies near 17 cycles day-1. Our results are found to be in good agreement with the theoretical limits imposed on the frequencies of oscillation by the models of Dziembowski (1990).

scholarly journals On the detection of stellar differential rotation based on the Fourier transform of spectral line profiles

2019 ◽  
Vol 72 (1) ◽  
Author(s):  
Yoichi Takeda
Keyword(s):  
Fourier Transform ◽  
Spectral Line ◽  
Differential Rotation ◽  
Fourier Transforms ◽  
Rotational Velocity ◽  
Model Atmosphere ◽  
Strict Sense ◽  
Line Profiles ◽  
Classical Formulation ◽  
The Fourier Transform

Abstract It is known that stellar differential rotation can be detected by analyzing the Fourier transform of spectral line profiles, since the ratio of the first and second zero frequencies is a useful indicator. This approach essentially relies on the conventional formulation that the observed flux profile is expressible as a convolution of the rotational broadening function and the intrinsic profile, which implicitly assumes that the local intensity profile does not change over the disk. Although this postulation is unrealistic in the strict sense, how the result is affected by this approximation is still unclear. With the aim of examining this problem, flux profiles of several test lines (showing different center-to-limb variations) were simulated using a model atmosphere corresponding to a mid-F dwarf by integrating the intensity profiles for various combinations of vesin i (projected rotational velocity), α (differential degree), and i (inclination angle), and their Fourier transforms were computed to check whether the zeros are detected at the predicted positions or not. For this comparison a large grid of standard rotational broadening functions and their transforms/zeros were also calculated. It turned out that the situation depends critically on vesin i: In the case of vesin i ≳ 20 km s−1, where rotational broadening is predominant over other line broadening velocities (typically several km s−1), the first/second zeros of the transform are confirmed almost at the expected positions. In contrast, deviations begin to appear as vesin i is lowered, and the zero features of the transform are totally different from those expected at vesin i as low as ∼10 km s−1, which means that the classical formulation is no longer valid. Accordingly, while the zero-frequency approach is safely applicable to studying differential rotation in the former broader-line case, it would be difficult to practice for the latter sharp-line case.

Two-Dimensional Fast Fourier Transform and Power Spectrum for Surface Roughness in three Dimensions

1995 ◽  
Vol 209 (5) ◽  
pp. 381-391 ◽  
Author(s):  
W P Dong ◽  
K J Stout
Keyword(s):  
Surface Roughness ◽  
Fourier Transform ◽  
Power Spectrum ◽  
Fast Fourier Transform ◽  
Surface Characterization ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Comprehensive Understanding ◽  
Extract Information

Two-dimensional power spectrums of engineering surfaces contain plenty of information that is important and valuable for surface characterization. However, the characteristics of the two-dimensional spectrums are largely unknown and the algorithm to implement them is not familiar to many engineers or researchers. This paper describes a detailed procedure to implement the two-dimensional fast Fourier transform and power spectrum for surface roughness in three dimensions. Methods used to extract information from the spectrums are introduced. In order to perform two-dimensional spectral analysis and to have a comprehensive understanding of the characteristics of engineering surfaces, an atlas of the two-dimensional spectrums of representative engineering surfaces are presented. The properties of the spectrums are discussed in conjunction with theoretical analysis and visual characterization of the presented spectrums.

Design of one-dimensional power spectrum using two-dimensional fast Fourier transform for discrimination of paper-based kraft tapes

2015 ◽  
Vol 257 ◽  
pp. 329-336 ◽  
Author(s):  
Sara Sasaoka ◽  
Koichi Saito ◽  
Kenjirou Higashi ◽  
Waree Limwikrant ◽  
Kunikazu Moribe ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Power Spectrum ◽  
Fast Fourier Transform ◽  
Two Dimensional ◽  
One Dimensional

scholarly journals On the Data Reduction of WET Observations

2003 ◽  
Vol 12 (4) ◽  
Author(s):  
Erika Pakštienė
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Power Spectrum ◽  
Extinction Coefficient ◽  
Continuous Time ◽  
Photometric Data ◽  
Order Effects ◽  
Correction Procedure ◽  
Atmospheric Extinction ◽  
Air Mass

AbstractIt is demonstrated how the length of a continuous time-series of photometric data and their gaps affect the power spectrum of a Fourier Transform of the data. It is shown that second order effects of the atmospheric extinction - the dependence of the extinction coefficient on spectral type of a star and on the air mass - cannot be ignored. The ignoring of these effects results in aliases at frequencies lower than 200 μHz. A modification of the extinction correction procedure is proposed.

Directional spectral analysis and filtering of geophysical maps

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1587-1591 ◽  
Author(s):  
Freyr Thorarinsson ◽  
Stefan G. Magnusson ◽  
Axel Bjornsson
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Power Spectrum ◽  
Two Dimensional ◽  
Directional Filtering ◽  
Gravity And Magnetic ◽  
The Fourier Transform ◽  
Map Data ◽  
Tectonic Features

The detection of linear anomalies in map data is facilitated by studying the two‐dimensional power spectrum, because the directivity of the energy in the map is preserved in the Fourier transform. The lineaments associated with individual peaks in the spectrum are then separated from the map data by directional filtering and studied independently of other map features. Gravity and magnetic maps from an active rift area in southwestern Iceland are analyzed in this manner. The agreement between the filtered maps is good and they fit the observed tectonic features quite well.

Studies on Automatic Recognition System of Fabric Weaves’ Parameters

2011 ◽  
Vol 341-342 ◽  
pp. 829-832 ◽  
Author(s):  
Yan Mei Li ◽  
Xiao Kun Qiu ◽  
Zhen Zhen Jiang
Keyword(s):  
Fourier Transform ◽  
Power Spectrum ◽  
Computer Image ◽  
Recognition System ◽  
Automatic Recognition ◽  
Image Process ◽  
Two Dimensional ◽  
Process Technology ◽  
Weave Pattern ◽  
In Virtue Of

In virtue of having some periodicity in space, the fabric weave pattern can be recognized by using computer image process technology. Firstly, the reflected image and transmissive image of fabric were scanned and disposed. Then its image of two-dimensional power spectrum and image of autocorrelation were obtained by means of Fourier transform technology. Finally the fabric weave parameters can be calculated, including density of warp and weft, the size of warp and weft and the yarn numbers of weave repetition etc. Based on foregoing theory, this paper develops automatic recognition system of fabric weave parameters, which is worth of popularizing.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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