A system with transfer function $H(z)$ has impulse response $h(\cdot)$ defined as $h(2)=1, h(3)=-1$ and $h(k)=0$ otherwise. Consider the following statements.
$\qquad \qquad \text{S1: } H(z)$ is a low-pass filter.
$\qquad \qquad \text{S2: } H(z)$ is an FIR filter.
Which of the following is correct?
- Only $\mathrm{S} 2$ is true
- Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are false
- Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are true, and $\mathrm{S} 2$ is a reason for $\mathrm{S} 1$
- Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are true, but $\mathrm{S} 2$ is not a reason for $\mathrm{S} 1$