ECE5606 Stochastic Signals and Systems
随机信号系统代考 Note: we know from problem 1 of HW1 that this process is stationary and, accordingly, its covariance function is given by:
1. Discuss whether the following functions can be covariance functions of a stationary stochastic process: 随机信号系统代考
Hint:The properties of the covariance function of a stationary process are: 随机信号系统代考
(a) |R(τ )| ≤ R(0)
(b) R(0)≥ 0
(c) |R(τ )| = R(0), for some τ = 0
(d) R(τ ) = R(−τ )
(e) if R(τ ) is continuous for τ = 0, then R(τ ) is continuous for all τ.
2. A stationary stochastic process has the covariance functions
Determine the corresponding spectral density functions.
- Determine the spectral 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. 随机信号系统代考
Note: we know from problem 1 of HW1 that this process is stationary and, accordingly, its covariance function is given by: