Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $\left[-\omega_c, \omega_c\right]$, where $\omega_c$ is in rad/sec.

The signal $f(t)$ is uniformly sampled to obtain $y(t)=f(t) p(t)$. Here

$$ p(t)=\sum_{n=-\infty}^{\infty} \delta\left(t-\tau-n T_s\right) $$

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 $h(t)=\omega_c T_s \frac{\sin \left(\omega_c t\right)}{\pi \omega_c t}$ with cutoff frequency $\omega_c$ and passband gain $T_s$.

The output of the filter is given by $\qquad$ .

A continuous time signal $x(t) = 2 \cos(8 \pi t + \frac{\pi}{3})$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response

$h(t) = \left( \frac{\sin 2 \pi t}{\pi t} \right) \cos(38 \pi t - \frac{\pi}{2})$

produces an output $x_o(t)$. The expression for $x_o(t)$ is ______.

What is the number of sinusoids in the output and their frequency inkHz?