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KianXrw974

We derive fashions that can convey residual biases to the p.c degree on small scales. We elucidate the affect of aliasing and the various shape of HEALPix pixels on energy spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose a number of enhancements to the usual estimator and its modelling, primarily based on the precept that supply positions and weights are to be considered fastened. We present how empty pixels may be accounted for both by modifying the mixing matrices or making use of correction components that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and present that it may well mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-restricted spectra, biases from using an isotropic window perform might be successfully diminished to zero. This work partly intends to serve as a helpful reference for pixel-associated results in angular energy spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.

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