相关论文: Gabor Transforms on the Sphere with Applications t…

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these…

We present a novel formalism to describe the $in$ $vacuo$ conversion between polarization states of propagating radiation, also known as generalized Faraday effect (GFE), in a cosmological context. Thinking of GFE as a potential tracer of…

The statistical properties of a map of the primary fluctuations in the cosmic microwave background (CMB) may be specified to high accuracy by a few thousand power spectra measurements, provided the fluctuations are gaussian, yet the number…

Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB.…

Most cosmic microwave background experiments observe the sky along circular or near-circular scans on the celestial sphere. For such experiments, we show that simple linear systems connect the Fourier spectra of temperature and polarization…

The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic effects, which become important on large scales. At the same time, wide-angle (WA) effects due to differing…

Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not…

Analyzing the internal loss characteristics and multimodedness of (integrated) optical devices can prove difficult. One technique to recover this information is to Fourier transform the transmission spectrum of optical components. This…

Earlier papers introduced a method of accurately estimating the angular cosmic microwave background (CMB) temperature power spectrum based on Gibbs sampling. Here we extend this framework to polarized data. All advantages of the Gibbs…

The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce…

The Cosmic Microwave Background (CMB) data analysis and the map-making process rely heavily on the use of spherical harmonics. For suitable pixelizations of the sphere, the (forward and inverse) Fourier transform plays a crucial role in…

A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a non-negative time parameter $t$. We show that the corresponding Gabor-like system forms a…

The most commonly used estimators of the anisotropic galaxy power spectrum employ Fast Fourier transforms, and rely on a specific choice of the line-of-sight that breaks the symmetry between the galaxy pair. This leads to wide-angle…

Precise, unbiased measurements of extragalactic background anisotropies require careful treatment of systematic effects in fluctuation-based, broad-band intensity mapping measurements. In this paper we detail improvements in methodology for…

To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to…

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example,…

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited…

I develop a method for assessing the ability of an instrument, coupled with an observing strategy, to measure the angular power spectrum of the cosmic microwave background (CMB). It allows for efficient calculation of expected parameter…

We introduce new Fourier band-power estimators for cosmic shear data analysis and E/B-mode separation. We consider both the case where one performs E/B-mode separation and the case where one does not. The resulting estimators have several…

We develop a pseudo power spectrum technique for measuring the lensing power spectrum from weak lensing surveys in both the full sky and flat sky limits. The power spectrum approaches have a number of advantages over the traditional…