  Fast radio bursts (FRBs) are short-duration radio transients of unknown
origin. Thus far, they have been blindly detected at millisecond timescales
with dispersion measures (DMs) between 110--2600\,pc\,cm$^{-3}$. However, the
observed pulse width, DM, and even brightness distributions depend strongly on
the time and frequency resolution of the detection instrument. Spectral and
temporal resolution also significantly affect FRB detection rates, similar to
beam size and system-equivalent flux density (SEFD). I discuss the interplay
between underlying FRB properties and instrumental response, and provide a
generic formalism for calculating the \textit{observed} distributions of
parameters given an intrinsic FRB distribution, focusing on pulse width and DM.
I argue that if there exist many FRBs of duration $<<$\,1\,ms (as with giant
pulses from Galactic pulsars) or events with high DM, they are being missed due
to the deleterious effects of smearing. I outline how to optimise spectral and
temporal resolution for FRB surveys that are throughput-limited. I also
investigate how such effects may have been imprinted on the distributions of
FRBs at real telescopes, like the different observed DMs at ASKAP and Parkes.
Finally, I discuss the impact of intrinsic correlations between FRB parameters
on detection statistics.
