Question

3. Given a random process \(X(t) = A \cos(\omega_0 t + \Theta)\) where \(\omega_0\) is the constant angular frequency, and A and \(\Theta\) are uniformly distributed over the ranges (-2, 2) and (-?, ?), respectively. Note that A and \(\Theta\) are two independent random variables. (a) Compute the expectation of X(t) and its autocorrelation function \(R_X(t_1, t_2)\). Is the process wide-sense stationary? (b) If the process is wide-sense stationary, determine and plot the power spectral density of X(t). (c) Draw 4 waveforms of X(t) for some possible values of A and \(\Theta\). Discuss whether the process is ergodic with your drawings.

          3.
Given a random process
\(X(t) = A \cos(\omega_0 t + \Theta)\)
where \(\omega_0\) is the constant angular frequency, and A and \(\Theta\) are uniformly distributed over
the ranges (-2, 2) and (-?, ?), respectively. Note that A and \(\Theta\) are two independent
random variables.
(a) Compute the expectation of X(t) and its autocorrelation function \(R_X(t_1, t_2)\). Is the
process wide-sense stationary?
(b) If the process is wide-sense stationary, determine and plot the power spectral
density of X(t).
(c) Draw 4 waveforms of X(t) for some possible values of A and \(\Theta\). Discuss whether
the process is ergodic with your drawings.

3.
Given a random process
X(t) = A cos(ω0 t + Θ)
where ω0 is the constant angular frequency, and A and Θ are uniformly distributed over
the ranges (-2, 2) and (-?, ?), respectively. Note that A and Θ are two independent
random variables.
(a) Compute the expectation of X(t) and its autocorrelation function RX(t1, t2). Is the
process wide-sense stationary?
(b) If the process is wide-sense stationary, determine and plot the power spectral
density of X(t).
(c) Draw 4 waveforms of X(t) for some possible values of A and Θ. Discuss whether
the process is ergodic with your drawings.

Added by Isabella G.

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