Understand
We review the methodology for measurements of two point functions of the cosmological observables, both power spectra and correlation functions.
- For pseudo-$C_\ell$ estimators, we will argue that the window weighted overdensity field can yield more optimal measurements as the window acts as an inverse noise weight, an effect that becomes more important for surveys with a variable selection function.
- We then discuss the impact of approximations made in the {\sc Master} algorithm and suggest improvements, the {\sc $i$Master} algorithm, that uses the theoretical model to give unbiased results for arbitrarily complex windows provided that the model satisfies weak accuracy conditions.
- The methodology of {\sc $i$Master} algorithm is also generalized to the correlation functions to reconstruct the binned power spectra, for E/B mode separation, or to properly convolve the correlation functions to account for the scale cuts in the Fourier space model.