Terence J. Deeming

Bio: Terence J. Deeming is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Fourier analysis & Fourier transform. The author has an hindex of 3, co-authored 4 publications receiving 749 citations.

Fourier analysis with unequally-spaced data*

Abstract: The general problems of Fourier and spectral analysis are discussed. A discrete Fourier transformF N (v) of a functionf(t) is presented which (i) is defined for arbitrary data spacing; (ii) is equal to the convolution of the true Fourier transform off(t) with a spectral window. It is shown that the ‘pathology’ of the data spacing, including aliasing and related effects, is all contained in the spectral window, and the properties of the spectral windows are examined for various kinds of data spacing. The results are applicable to power spectrum analysis of stochastic functions as well as to ordinary Fourier analysis of periodic or quasiperiodic functions.

Spurious results from Fourier analysis of data with closely spaced frequencies

Abstract: It is shown how erroneous results can occur using some period-finding methods, such as Fourier analysis, on data containing closely spaced frequencies The frequency spacing accurately resolvable with data of lengthT is increased from the standard value of about 1/T quoted in the literature to approximately 15/T

The Application of a Bessel Transform to the Determination of Stellar Rotational Velocities

Abstract: A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocityv sini, to an accuracy of about ±1 km s−1 for rotational velocities greater than about 5 km s−1, provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix.

Remarks on the restoration of occultation observations.

Abstract: If the limb of the Moon can be regarded as a straight edge, then the diffraction pattern of a point source which it produces at the distance of the Earth is the well known Fresnel diffraction pattern. Observations of stellar occultations reveal the variation of intensity with time as the diffraction pattern passes across the detector due to the orbital motion of the Moon and the rotation of the Earth. The linear scale of the diffraction pattern in monochromatic light depends on both the wavelength of observation, λ, and on the distance of the Moon,D, so that the scale is proportional to (λ)1/2.

A box-fitting algorithm in the search for periodic transits

Abstract: We study the statistical characteristics of a box-fitting algorithm to analyze stellar photometric time series in the search for periodic transits by extrasolar planets. The algorithm searches for signals characterized by a periodic alternation between two discrete levels, with much less time spent at the lower level. We present numerical as well as analytical results to predict the possible detection significance at various signal parameters. It is shown that the crucial parameter is the eective signal-to-noise ratio - the expected depth of the transit divided by the standard deviation of the measured photometric average within the transit. When this parameter exceeds the value of 6 we can expect a significant detection of the transit. We show that the box-fitting algorithm performs better than other methods available in the astronomical literature, especially for low signal-to-noise ratios.

A box-fitting algorithm in the search for periodic transits

Abstract: We study the statistical characteristics of a box-fitting algorithm to analyze stellar photometric time series in the search for periodic transits by extrasolar planets. The algorithm searches for signals characterized by a periodic alternation between two discrete levels, with much less time spent at the lower level. We present numerical as well as analytical results to predict the possible detection significance at various signal parameters. It is shown that the crucial parameter is the effective signal-to-noise ratio -- the expected depth of the transit divided by the standard deviation of the measured photometric average within the transit. When this parameter exceeds the value of 6 we can expect a significant detection of the transit. We show that the box-fitting algorithm performs better than other methods available in the astronomical literature, especially for low signal-to-noise ratios.

Understanding the Lomb–Scargle Periodogram

Abstract: The Lomb-Scargle periodogram is a well-known algorithm for detecting and characterizing periodic signals in unevenly-sampled data. This paper presents a conceptual introduction to the Lomb-Scargle periodogram and important practical considerations for its use. Rather than a rigorous mathematical treatment, the goal of this paper is to build intuition about what assumptions are implicit in the use of the Lomb-Scargle periodogram and related estimators of periodicity, so as to motivate important practical considerations required in its proper application and interpretation.

Measuring the broad-band power spectra of active galactic nuclei with RXTE

Abstract: We develop a Monte Carlo technique to test models for the true power spectra of intermittently sampled light curves against the noisy, observed power spectra, and produce a reliable estimate of the goodness of fit of the given model. We apply this technique to constrain the broad-band power spectra of a sample of four Seyfert galaxies monitored by the Rossi X-ray Timing Explorer (RXTE ) over three years. We show that the power spectra of three of the AGN in our sample (MCG-6-30-15, NGC 5506 and NGC 3516) flatten significantly towards low frequencies, while the power spectrum of NGC 5548 shows no evidence of flattening. We fit two models for the flattening: a 'knee' model, analogous to the low-frequency break seen in the power spectra of BHXRBs in the low state (where the power-spectral slope flattens to α =0), and a 'high-frequency break' model (where the power-spectral slope flattens to α =1), analogous to the high-frequency break seen in the high- and low-state power spectra of the classic BHXRB Cyg X-1. Both models provide good fits to the power spectra of all four AGN. For both models, the characteristic frequency for flattening is significantly higher in MCG-6-30-15 than in NGC 3516 (by a factor of ~10), although both sources have similar X-ray luminosities, suggesting that MCG-6-30-15 has a lower black hole mass and is accreting at a higher rate than NGC 3516. Assuming linear scaling of characteristic frequencies with black hole mass, the high accretion rate implied for MCG-6-30-15 favours the high-frequency break model for this source, and further suggests that MCG-6-30-15, and possibly NGC 5506, may be analogues of Cyg X-1 in the high state. Comparison of our model fits with naive fits, where the model is fitted directly to the observed power spectra (with errors estimated from the data), shows that Monte Carlo fitting is essential for reliably constraining the broad-band power spectra of AGN light curves obtained to date.

Eit observations of the extreme ultraviolet sun

Abstract: The Extreme Ultraviolet Imaging Telescope (EIT) on board the SOHO spacecraft has been operational since 2 January 1996. EIT observes the Sun over a 45 × 45 arc min field of view in four emission line groups: Fe IX, X, Fe XIIi, Fe xv, and He II. A post-launch determination of the instrument flatfield, the instrument scattering function, and the instrument aging were necessary for the reduction and analysis of the data. The observed structures and their evolution in each of the four EUV bandpasses are characteristic of the peak emission temperature of the line(s) chosen for that bandpass. Reports on the initial results of a variety of analysis projects demonstrate the range of investigations now underway: EIT provides new observations of the corona in the temperature range of 1 to 2 MK. Temperature studies of the large-scale coronal features extend previous coronagraph work with low-noise temperature maps. Temperatures of radial, extended, plume-like structures in both the polar coronal hole and in a low latitude decaying active region were found to be cooler than the surrounding material. Active region loops were investigated in detail and found to be isothermal for the low loops but hottest at the loop tops for the large loops.