Remark on the estimation of angular power spectra in the presence of foregrounds

Abstract

It is common practice to estimate the errors on the angular power spectrum which could be obtained by an experiment with a given angular resolution and noise level. Several authors have also addressed the question of foreground subtraction using multi-frequency observations. In such observations the angular resolution of the different frequency channels is rarely the same. In this report we point out how the ``effective'' beam size and noise level change with $l$ in this case, and give an expression for the error on the angular power spectrum as a function of $l$.