Question

A wide-sense stationary random process $X(t)$ is Gaussian, has zero mean, and has a power spectral density shown below. $S_x(f)$ 1 0.5 f (Hz) -300 -100 100 300 (a) Find the standard deviation of the random process $X(t)$ (b) The random process $X(t)$ in (a) is passed through an ideal lowpass filter with gain equal to 4.0 and passband extending from -160 Hz to +160 Hz. If $Y(t)$ is the output of the filter, and its mean and plot its power spectral density.

          A wide-sense stationary random process $X(t)$ is Gaussian, has
zero mean, and has a
power spectral density shown below.
$S_x(f)$
1
0.5
f (Hz)
-300
-100
100
300
(a) Find the standard deviation of the random process $X(t)$
(b) The random process $X(t)$ in (a) is passed through an ideal
lowpass filter with gain equal to 4.0 and passband
extending from -160 Hz to +160 Hz. If $Y(t)$ is the output of
the filter, and its mean and plot its power spectral density.

A wide-sense stationary random process X(t) is Gaussian, has
zero mean, and has a
power spectral density shown below.
Sx(f)
1
0.5
f (Hz)
-300
-100
100
300
(a) Find the standard deviation of the random process X(t)
(b) The random process X(t) in (a) is passed through an ideal
lowpass filter with gain equal to 4.0 and passband
extending from -160 Hz to +160 Hz. If Y(t) is the output of
the filter, and its mean and plot its power spectral density.

Added by James P.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert Patricia Holmes

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A wide-sense stationary random process X is Gaussian, has zero mean, and has a power spectral density shown below. Sx(f) = 0.5 for -100Hz â‰¤ f â‰¤ 100Hz and Sx(f) = 0 for |f| > 100Hz. (a) Find the standard deviation of the random process Xt. (b) The random process Xt is passed through an ideal lowpass filter with gain equal to 4.0 and passband extending from -160Hz to +160Hz. If Y(t) is the output of the filter, find its mean and plot its power spectral density.