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Over the last few years, needlets have a emerged as a useful tool for theanalysis of Cosmic Microwave Background (CMB) data. Our aim in this paper isfirst to introduce in the CMB literature a different form of needlets, known asMexican needlets, first discussed in the mathematical literature by Geller andMayeli (2009a,b). We then proceed with an extensive study of the properties ofboth standard and Mexican needlets; these properties depend on some parameterswhich can be tuned in order to optimize the performance for a givenapplication. Our second aim in this paper is then to give practical advice onhow to adjust these parameters in order to achieve the best properties for agiven problem in CMB data analysis. In particular we investigate localizationproperties in real and harmonic spaces and propose a recipe on how to quantifythe influence of galactic and point source masks on the needlet coefficients.We also show that for certain parameter values, the Mexican needlets provide aclose approximation to the Spherical Mexican Hat Wavelets (whence their name),with some advantages concerning their numerical implementation and thederivation of their statistical properties.

Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets