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 $\qquad$ .

Let $f(t)$ be a periodic signal with fundamental period $T_0>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$.

The Fourier series expansions of $f(t)$ and $y(t)$ are given by

$$ f(t)=\sum\limits_{k = - \infty }^\infty c_k e^{j \frac{2 \pi}{T_0} k T} \text { and } y(t)=\sum\limits_{k = - \infty }^\infty d_k e^{j \frac{2 \pi}{T_0} \alpha k T} . $$

Which of the following statements is/are TRUE?

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.

Group-I: Abuse $\rightarrow$ Insult $\rightarrow$ Ridicule

Group-II: __________$\rightarrow$ Praise $\rightarrow$ Appreciate