Journal Article

A Mexican hat with holes: calculating low-resolution power spectra from data with gaps

P. Arévalo, E. Churazov, I. Zhuravleva, C. Hernández-Monteagudo and M. Revnivtsev

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 426, issue 3, pages 1793-1807
Published in print November 2012 | ISSN: 0035-8711
Published online November 2012 | e-ISSN: 1365-2966 | DOI:
A Mexican hat with holes: calculating low-resolution power spectra from data with gaps

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A simple method for calculating a low-resolution power spectrum from data with gaps is described. The method is a modification of the Δ-variance method previously described by Stutzki and Ossenkopf. A Mexican hat filter is used to single out fluctuations at a given spatial scale, and the variance of the convolved image is calculated. The gaps in the image, defined by the mask, are corrected for by representing the Mexican hat filter as a difference between two Gaussian filters with slightly different widths, convolving the image and mask with these filters and dividing the results before calculating the final filtered image. This method cleanly compensates for data gaps even if these have complicated shapes and cover a significant fraction of the data. The method was developed to deal with problematic 2D images, where irregular detector edges and masking of contaminating sources compromise the power spectrum estimates, but it can also be straightforwardly applied to 1D timing analysis or 3D data cubes from numerical simulations.

Keywords: methods: data analysis; galaxies: active; galaxies: clusters: general

Journal Article.  10953 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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