Tidal turbine reliability is strongly affected by fluctuating loads induced by turbulence and waves at tidal energy sites. Turbulence is most often characterised through its intensity, which is the turbulent kinetic energy (TKE) scaled by the mean flow speed. The most common instrument for measuring TKE is the acoustic Doppler current profiler; however, the estimate from this instrument is intrinsically contaminated by wave action, and in fact wave action may completely swamp the true turbulence. We describe a statistical signal separation method based on empirical orthogonal function analysis, and apply it to a test case that performs well in separating the true TKE from the pseudo-TKE induced by the waves. The validity of the method is tested against estimates from linear theory, using wave state parameters from a wave buoy operating independently of the profiler. We find that estimates are very well-correlated with one another, but error between theoretical and statistical estimates of wave action can appear very high unless low wave height conditions are excluded. A decomposition of the original TKE estimate into wave and turbulence components, based only on the profiler data, is presented.