ECE5606 Stochastic Signals and Systems: HW 2
代写信息系统作业 Determinethespectral density of the process x(t) = e(t) + ce(t − 1) where e(t) t = . . . , −1, 0, 1, . . . } is a sequence of
Due Monday, 21 February 2022
1. Discusswhetherthe following functions can be covariance functions of a sta- tionary stochastic process: 代写信息系统作业
Hint:The properties of the covariance function of a stationary process are:
(a) |R(τ)| ≤ R(0)
(b) R(0)≥ 0
(c) |R(τ)| = R(0), for some τ 0 代写信息系统作业
(d) R(τ) = R(−τ)
(e) if R(τ) is continuous for τ = 0, then R(τ) is continuous for all τ .
2. Astationarystochastic process has the covariance functions
Determine the corresponding spectral density functions.
3. Determinethespectral density of the process x(t) = e(t) + ce(t − 1) where e(t) t = . . . , −1, 0, 1, . . . } is a sequence of independent normal (0, 1) random variables. 代写信息系统作业
Note: we know from problem 1 of HW1 that this process is stationary and, accordingly, its covariance function is given by:
4. Adynamicalsystem is governed by the stochastic difference
where {e(t),t ∈ T} is a stochastic sequence of independent normal (0, 1) stochas- tic variables. Determine the covariance of the steady state distribution.
发表回复
要发表评论，您必须先登录。