  We consider the nonparametric estimation of a periodic function that is
observed in additive Gaussian white noise after convolution with a ``boxcar,''
the indicator function of an interval. This is an idealized model for the
problem of recovery of noisy signals and images observed with ``motion blur.''
If the length of the boxcar is rational, then certain frequencies are
irretreviably lost in the periodic model. We consider the rate of convergence
of estimators when the length of the boxcar is irrational, using classical
results on approximation of irrationals by continued fractions. A basic
question of interest is whether the minimax rate of convergence is slower than
for nonperiodic problems with 1/f-like convolution filters. The answer turns
out to depend on the type and smoothness of functions being estimated in a
manner not seen with ``homogeneous'' filters.
