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Let $X(t)$ be a wide sense stationary $(WSS)$ random process with power spectral density $S_{X}(f).$ If $Y(t)$ is the process defined as $Y(t)= X(2t-1)$, the power spectral density $S_{Y}( f )$ is

  1. $S_{Y}( f )= \frac{1}{2}S_{X}\left ( \frac{f}{2} \right )e^{-j\pi f}$
  2. $S_{Y}( f )= \frac{1}{2}S_{X}\left ( \frac{f}{2} \right )e^{-j\pi f/2}$
  3. $S_{Y}( f )= \frac{1}{2}S_{X}\left ( \frac{f}{2} \right )$
  4. $S_{Y}( f )= \frac{1}{2}S_{X}\left ( \frac{f}{2} \right )e^{-j2\pi f }$
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