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An input signal $x(t)=2+5 \sin(100\pi t)$  is sampled with a sampling frequency of $400$ $Hz$ and applied to the system whose transfer function is represented by $$\dfrac{Y(z)}{X(z)}=\dfrac{1}{N} \bigg (\dfrac{1-Z^{-N}}{1-Z^{-1}} \bigg)$$ where, $N$ represents the number of samples per cycle. The output $y(n)$ of the system under steady state is

  1. $0$
  2. $1$
  3. $2$
  4. $5$
in Signals and Systems by (9.3k points)
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