  We consider the problem of recovering a continuous-time bandlimited signal
from the discrete-time signal obtained from sampling it every $T_s$ seconds and
reducing the result modulo $\Delta$, for some $\Delta>0$. For $\Delta=\infty$
the celebrated Shannon-Nyquist sampling theorem guarantees that perfect
recovery is possible provided that the sampling rate $1/T_s$ exceeds the
so-called Nyquist rate. Recent work by Bhandari et al. has shown that for any
$\Delta>0$ perfect reconstruction is still possible if the sampling rate
exceeds the Nyquist rate by a factor of $\pi e$. In this letter we improve upon
this result and show that for finite energy signals, perfect recovery is
possible for any $\Delta>0$ and any sampling rate above the Nyquist rate. Thus,
modulo folding does not degrade the signal, provided that the sampling rate
exceeds the Nyquist rate. This claim is proved by establishing a connection
between the recovery problem of a discrete-time signal from its modulo reduced
version and the problem of predicting the next sample of a discrete-time signal
from its past, and leveraging the fact that for a bandlimited signal the
prediction error can be made arbitrarily small.
