List of top Signals and Systems Questions on Impulse response of systems asked in GATE BM

The output \(y[n]\) of a digital moving average filter for an input \(x[n]\) is given by
\[ y[n] = \frac{1}{4}\big(x[n] + 2x[n-1] + x[n-2]\big) \]
Which one of the following options is a correct statement about the transfer function of this filter?

A unit step input is applied to a system with impulse response \( H(s) = \dfrac{1-s/\omega_z}{1+s/\omega_p} \) at \( t = 0 \). The output of the system \( y(t) \) at \( t = 0^+ \) is