The three-dimensional spatial filtering and measurement noise associated with experimental planar and three-dimensional (3D) particle image velocimetry (PIV) measurements is investigated using a combination of direct numerical simulations (DNS) and experimental databases. Spatial filtering velocity fields from a DNS of a zero-pressure-gradient turbulent boundary layer (TBL) at resolutions typical of PIV experiments are shown to underestimate Reynolds stresses by as much as 50 %. Comparison of experimental PIV measurement of a turbulent channel flow and 3D tomographic PIV measurements of a TBL with higher-resolution simulations and hotwire anemometry measurements show that in real experiments, measurement noise acts to offset this effect. This is shown to produce measurements that appear to provide a good estimate of the turbulent fluctuations in the flow, when in reality the flow is spatially under-resolved and partially contaminated by noise. Means of identifying this noise are demonstrated using the one-dimensional (1D) velocity power spectra and the 1D transfer function between the power spectra of the unfiltered velocity field and the power spectra calculated from the filtered experimental measurement. This 1D transfer function differs from the commonly used sinc transfer function of PIV owing to the integrated effect of filtering in multiple directions. Failure to incorporate this difference is shown to overestimate the maximum resolved wave number in the 3D spectra of the planar PIV by close to 10 %, while conversely underestimating the maximum resolved wave number in the 3D PIV by 50 %. Appropriate spatial filtering of the experimental data is shown to remove the noise-dominated small-scale fluctuations and bring the data inline with that which should be obtained for a noiseless PIV measurement at the corresponding spatial resolution.