Let x(t) be a wide sense stationary (WSS) random 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

A) $${S_Y}\left( f \right) = {1 \over 2}{S_X}\left( {{f \over 2}} \right){e^{ - j\pi t}}$$ B) $${S_Y}\left( f \right) = {1 \over 2}{S_X}\left( {{f \over 2}} \right){e^{ - {{j\pi t} \over 2}}}$$ C) $${S_Y}\left( f \right) = {1 \over 2}{S_X}\left( {{f \over 2}} \right)$$ D) $${S_Y}\left( f \right) = {1 \over 2}{S_X}\left( {{f \over 2}} \right){e^{j2\pi f}}$$

Answer & Solution

Correct Answer: Option C

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Let x(t) be a wide sense stationary (WSS) random with power...

Let x(t) be a wide sense stationary (WSS) random with power spectral density Sx(f). If Y(t) is the process defined as y(t) = x(2t - 1), the power spectral density SY(f) is

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Let x(t) be a wide sense stationary (WSS) random 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