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We review the methodology for measurements of two point functions of thecosmological observables, both power spectra and correlation functions. Forpseudo-$C_\ell$ estimators, we will argue that the window weighted overdensityfield can yield more optimal measurements as the window acts as an inversenoise weight, an effect that becomes more important for surveys with a variableselection 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 arbitrarilycomplex windows provided that the model satisfies weak accuracy conditions. Themethodology of {\sc $i$Master} algorithm is also generalized to the correlationfunctions to reconstruct the binned power spectra, for E/B mode separation, orto properly convolve the correlation functions to account for the scale cuts inthe Fourier space model. We also show that the errors in the window estimationlead to both additive and multiplicative effects on the over density field.Multiplicative effects show up as mis-estimated window power and are typicallyhigher order but can be important at the few percent precision requirements.Accurate estimation of window power can be required up to scales of $\sim2\ell_\text{max}$ or larger. Misestimation of the window power leads to biasesin the measured power spectra which scale as ${\delta C_\ell}\simM^W_{\ell\ell'}\delta W_{\ell'}$, where the $M^W_{\ell\ell'}$ scales as$\sim(2\ell+1)C_\ell$ leading to effects that can be important at high $\ell$.While the notation in this paper is geared towards photometric galaxy surveys,the discussion is equally applicable to spectroscopic galaxy, intensity mappingand CMB surveys.

Improved Master for the LSS: Fast and accurate analysis of the two point power spectra and correlation functions