Consider a continuous-time finite-energy signal \( f(t) \) whose Fourier transform vanishes outside the frequency interval \( [-\omega_c, \omega_c] \), where \( \omega_c \) is in rad/sec.
The signal \( f(t) \) is uniformly sampled to obtain \( y(t) = f(t) p(t) \). Here,
\[
p(t) = \sum_{n=-\infty}^{\infty} \delta(t - \tau - nT_s),
\]
with \( \delta(t) \) being the Dirac impulse, \( T_s > 0 \), and \( \tau > 0 \). The sampled signal \( y(t) \) is passed through an ideal lowpass filter \( h(t) = \omega_c T_s \frac{\sin(\omega_c t)}{\pi \omega_c t} \) with cutoff frequency \( \omega_c \) and passband gain \( T_s \).
The output of the filter is given by _________.
