  Combining the visibilities measured by an interferometer to form a
cosmological power spectrum is a complicated process. In a delay-based
analysis, the mapping between instrumental and cosmological space is not a
one-to-one relation. Instead, neighbouring modes contribute to the power
measured at one point, with their respective contributions encoded in the
window functions. To better understand the power measured by an interferometer,
we assess the impact of instrument characteristics and analysis choices on
these window functions. Focusing on the Hydrogen Epoch of Reionization Array
(HERA) as a case study, we find that long-baseline observations correspond to
enhanced low-k tails of the window functions, which facilitate foreground
leakage, whilst an informed choice of bandwidth and frequency taper can reduce
said tails. With simple test cases and realistic simulations, we show that,
apart from tracing mode mixing, the window functions help accurately
reconstruct the power spectrum estimator of simulated visibilities. The window
functions depend strongly on the beam chromaticity, and less on its spatial
structure - a Gaussian approximation, ignoring side lobes, is sufficient.
Finally, we investigate the potential of asymmetric window functions,
down-weighting the contribution of low-k power to avoid foreground leakage. The
window functions presented here correspond to the latest HERA upper limits for
the full Phase I data. They allow an accurate reconstruction of the power
spectrum measured by the instrument and will be used in future analyses to
confront theoretical models and data directly in cylindrical space.
