  After a successful supernova, a proto-neutron star (PNS) cools by emitting
neutrinos on $\sim 1-100$ s timescales. Provided that there are neutrino
emission `hot-spots' or `cold-spots' on the surface of the rotating PNS, we can
expect a periodic modulation in the number of neutrinos observable by
detectors. We show that Fourier transform techniques can be used to determine
the PNS rotation rate from the neutrino arrival times. Provided there is no
spindown, a 1-parameter Discrete Fourier Transform (DFT) is sufficient to
determine the spin period of the PNS. If the PNS is born as a magnetar with
polar magnetic field strength $B_0 \gtrsim 10^{15}$ G and is `slowly' rotating
with an initial spin period $\gtrsim 100$ ms, then it can spindown to periods
of the order of seconds during the cooling phase. We propose a modified DFT
technique with three frequency parameters to detect spindown. Due to lack of
neutrino data from a nearby supernova except the $\sim20$ neutrinos detected
from SN1987A, we use toy models and one physically motivated modulating
function to generate neutrino arrival times. We use the false alarm rate (FAR)
to quantify the significance of the Fourier power spectrum peaks. We show that
PNS rotation and spindown are detected with $\rm FAR<2\%$ ($2\sigma$) for
periodic signal content $\rm M\gtrsim 13-15\%$ if $5\times 10^{3}$ neutrinos
are detected in $\sim 3$ s and with $\rm FAR<1\%$ for $\rm M\geq 5\%$ if
$5\times 10^{4}$ neutrinos are detected in $\sim 3$ s. Since we can expect
$\sim 10^{4}-10^{5}$ neutrino detections from a supernova at 10 kpc, detection
of PNS rotation and spindown is possible using the neutrinos from the next
Galactic supernova.
