Multiple choice

X(t) is a stationary random process with autocorrelation function Rx($\tau$) = exp $(\pi r^2)$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

  1. $(4 \pi ^2 f^2 + 1) exp (-\pi t^2)$
  2. $(4 \pi ^2 f^2 - 1) exp (-\pi t^2)$
  3. $(4 \pi ^2 f^2 + 1) exp (-\pi f)$
  4. $(4 \pi ^2 f^2 - 1) exp (-\pi f)$
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A Correct answer
Explanation