ECE5606 Stochastic Signals and Systems:
随机信号系统代写 where the initial state is normal (0, 1). Is the process ergodic? Give a predictor for the process which predicts x(t + h) based
1. Consider the moving average process of order one x(t) = e(t) + ce(t − 1) where e(t) t = . . . , −1, 0, 1, . . . } is a sequence of independent normal (0, 1) random variables. 随机信号系统代写
(a) Determine the covariance of x(t) and x(s).
(b) Is the process stationary, normal, Markovian, ergodic, singular?
(c) Does the process have the independent increments?
2. Prove that
where x and y are stochastic processes and A, B, a and b are deterministic matrices and vectors, respectively.
3. Consider the singular stochastic process {x(t), 0 ≤ t < ∞} defined by 随机信号系统代写
where the initial state is normal (0, 1). Is the process ergodic? Give a predictor for the process which predicts x(t + h) based on measurements of x(t).
4. Consider the stochastic process 随机信号系统代写
where the initial state is normal with zero mean value and the covariance 随机信号系统代写
Is the process ergodic? Give a predictor for the process which predicts x(t + h) based on observation of {x1(t), t0 ≤ s ≤ t}.
Hint: The solution of the state of the system is given by x(t) = Φ(t, 0)x(0),
where 随机信号系统代写
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