  In practice most functional data cannot be recorded on a continuum, but
rather at discrete time points. It is also quite common that these measurements
come with an additive error, which one would like eliminate for the statistical
analysis. When the measurements for each functional datum are taken on the same
grid, the underlying signal-plus-noise model can be viewed as a factor model.
The signals refer to the common components of the factor model, the noise is
related to the idiosyncratic components. We formulate a framework which allows
to consistently recover the signal by a PCA based factor model estimation
scheme. Our theoretical results hold under rather mild conditions, in
particular we don't require specific smoothness assumptions for the underlying
curves and allow for a certain degree of autocorrelation in the noise.
