The lifespan of a tidal turbine is strongly affected by the unsteady loading it experiences, so knowledge of the mean flow speed is not sufficient: unsteadiness must also be quantified. One of the most common turbulence measurement devices in the marine environment is the Acoustic Doppler Current Profiler (ADCP). The variance of steady velocity measurements from ADCPs has been studied in detail, but very little attention has been given to the fundamental limits of ADCPs in terms of the frequencies and lengthscales that they can capture. In this paper, it is shown that the ADCP acts as a low-pass filter to eddies and that even optimistic calculations predict significant attenuation at lengthscales up to ten times the blade chord of a typical tidal turbine. For a typical 40 m deep channel wavelengths below 3-4 m are attenuated by 90% or more. Those eddies that are not filtered out are then subject to a distortion that will either amplify or attenuate the signal depending on the precise turbulence characteristics of the site in question. While this low-pass filtering may alter some global statistics by truncating the observed spectrum, it is most damaging when data is extracted for particular frequencies, as a turbine designer may do when assessing unsteady loading and fatigue life. It is therefore recommended that high-resolution turbulence data, e.g. from a hotwire, is captured over part of the water column and that this is used to calibrate ADCP data.