Methods for detection and characterization of signals in noisy data with the Hilbert-Huang Transform

The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the HHT with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal to noise ratio.Comment: submitted to PRD, 10 pages, 9 figures in colo

Complex Visibilities of Cosmic Microwave Background Anisotropies

We study the complex visibilities of the cosmic microwave background anisotropies that are observables in interferometric observations of the cosmic microwave background, using the multipole expansion methods commonly adopted in analyzing single-dish experiments. This allows us to recover the properties of the visibilities that is obscured in the flat-sky approximation. Discussions of the window function, multipole resolution, instrumental noise, pixelization, and polarization are given.Comment: 22 pages, 1 figure include

Robust Gravitational Wave Burst Detection and Source Localization in a Network of Interferometers Using Cross Wigner Spectra

We discuss a fast cross-Wigner transform based technique for detecting gravitational wave bursts, and estimating the direction of arrival, using a network of (three) non co-located interferometric detectors. The performances of the detector as a function of signal strength and source location, and the accuracy of the direction of arrival estimation are investigated by numerical simulations.Comment: accepted in Class. Quantum Gravit

Orthogonal sets of data windows constructed from trigonometric polynomials

Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given. Trigonometric coefficients and energy leakages of the window polynomials are tabulated

Supermassive Black Hole Mass Estimates Using Sloan Digital Sky Survey Quasar Spectra at 0.7 < z < 2

We present MgII-based black hole mass estimates for 27,602 quasars with rest-frame UV spectra available in the Sloan Digital Sky Survey Data Release Three. This estimation is possible due to the existence of an empirical correlation between the radius of the broad line region and the continuum luminosity at 3000 Angstroms. We regenerate this correlation by applying our measurement method to UV spectra of low-redshift quasars in the HST/IUE databases which have corresponding reverberation mapping estimates of the Hbeta broad line region's radius. Our mass estimation method uses the line dispersion rather than the full width at half maximum of the low-ionization MgII emission line. We measure MgII line dispersions for quasars whose spectra have been reconstructed using the most significant eigenspectra produced through Principal Component Analysis. We have tested the reliability of using reconstructed spectra in black hole mass estimation using a Monte Carlo simulation and by comparing the results from original and reconstructed Data Release Three spectra. We show that using reconstructed spectra not only makes bias-free mass estimation possible for quasars with low spectroscopic signal-to-noise ratio, but also reduces the intrinsic scatter of the distribution of the black hole masses to lower than 0.15 dex.Comment: 38 Pages, 12 figures, 3 Tables, 1 hyperlink to catalogue data. Accepted for publication in ApJ