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Electrical Engineering QUESTION #2184
Question 1
A causal LTI system has impulse response $h[n] = (0.5)^n u[n]$ and is excited by a unit step $x[n] = u[n]$. The steady-state output value is:
  • $2$✔️
  • $1$
  • $0.5$
  • $\infty$
Correct Answer Explanation
DC gain $H(e^{j0}) = \sum_{n=0}^{\infty}(0.5)^n = \frac{1}{1-0.5} = 2$. For a unit step (DC magnitude $= 1$), steady-state output $= 2\times1 = 2$.