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GATE 2014 EE (EE2) – Question 44

Signals and Systems · Fourier series representation of continuous and discrete time periodic signals, Sampling theorem · 2 marks · Multiple choice

$x(t)=2+5\sin(100\pi t)$ is sampled at 400 Hz and applied to $Y(z)/X(z)=(1-z^{-N})/[N(1-z^{-1})]$, where N is samples per cycle. Find steady-state y[n].

  1. 0
  2. 1
  3. 2
  4. 5

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Correct answer: (C) 2

Explanation

The sinusoid has50Hzfrequency and is sampled at400Hz,so N=8samples per cycle. The transfer function is(1/8)Σk=0^7z^(−k),an8sample moving average. It passes the constant2with unity gain and averages one complete sinusoidal cycle to zero. Therefore the steady output is **2,C**.