  We present a formalism to extract the angular power spectrum of fields
sampled at a finite number of points with arbitrary positions -- a common
situation for several catalog-based astrophysical probes -- through a simple
extension of the standard pseudo-$C_\ell$ algorithm. A key complication in this
case is the need to handle the shot noise component of the associated discrete
angular mask which, for sparse catalogs, can lead to strong coupling between
very different angular scales. We show that this problem can be solved easily
by estimating this contribution analytically and subtracting it. The resulting
estimator is immune to small-scale pixelization effects and aliasing, and, more
interestingly, unbiased against the contribution from measurement noise
uncorrelated between different sources. We demonstrate the validity of the
method in the context of cosmic shear datasets, and showcase its usage in the
case of other spin-0 and spin-1 astrophysical fields of interest. We
incorporate the method in the public $\texttt{NaMaster}$ code
(https://github.com/LSSTDESC/NaMaster).
