Consider the two continuous-time signals defined below:
$$x_1(t) = \begin{cases} \mid t \mid, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases} \\ x_2(t) = \begin{cases} 1 – \mid t \mid , & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases}$$
These signals are sampled with a sampling period of $T=0.25$ seconds to obtain discrete-time signals $x_1[n]$ and $x_2[n]$, respectively. Which one of the following statements is true?
- The energy of $x_1[n]$ is greater than the energy of $x_2[n]$
- The energy of $x_2[n]$ is greater than the energy of $x_1[n]$
- $x_1[n]$ and $x_2[n]$ have equal energies
- Neither $x_1[n]$ nor $x_2[n]$ is a finite-energy signal
