Looking for a solution to the following problem:
A signal $x(t)$ is band limited to $B$ Hz, and sampled above the Nyquist rate, with corresponding $f_s = 1/T$. If the sampled signal is given by
$$ y(n) = x(nT), $$
describe how to compute the phase-shifted sampled signal
$$ z(n) = x(nT + T/2), $$
from the samples $y(n)$ without first reconstructing $x(t)$ from $y(n)$ and resampling.
Have not been able to find one on the web.