Howtosignalprocessing
- How do you know if a random process is stationary?
- What is wide-sense random process?
- What is the difference between strict-sense stationary and wide-sense stationary?
- Is the Poisson random process wide-sense stationary?
How do you know if a random process is stationary?
Intuitively, a random process X(t),t∈J is stationary if its statistical properties do not change by time. For example, for a stationary process, X(t) and X(t+Δ) have the same probability distributions. In particular, we have FX(t)(x)=FX(t+Δ)(x), for all t,t+Δ∈J.
What is wide-sense random process?
Wide-Sense Stationary Random Processes. • A random process X(t) is said to be wide-sense stationary (WSS) if its mean. and autocorrelation functions are time invariant, i.e., ◦ E(X(t)) = µ, independent of t. ◦ RX(t1,t2) is a function only of the time difference t2 − t1.
What is the difference between strict-sense stationary and wide-sense stationary?
According to the definition (by Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel in "Synchronization, Channel Estimation, and Signal Processing") : strict-sense SP = not time dependent. wide-sense SP = not dependent on variable t (time)
Is the Poisson random process wide-sense stationary?
Such processes are called wide-sense stationary (wss). If a process is wss then its mean, variance, autocorrelation function and other first and second order statistical measures are independent of time. We have seen that a Poisson random process has mean µ(t) = λt, so it is not stationary in any sense. wss process.
