What is wide sense stationary random process?

What is wide sense stationary 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.

Is every strict-sense stationary process is a wide sense stationary process?

) and has finite second moments, then it is also wide-sense stationary. If a stochastic process is wide-sense stationary, it is not necessarily second-order stationary. If a stochastic process is strict-sense stationary and has finite second moments, it is wide-sense stationary.

What makes a random process 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.

What makes a random process a wide sense stationary process?

• 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

How is Y ( T ) wide sense stationary?

Let X ( t) be a wide sense stationary Gaussian random process and form a new process according to Y ( t) = X ( t) cos (ω t + Θ) where ω is a constant and Θ is a random variable uniformly distributed over [0, 2π) and independent of X ( t ). Is Y ( t) wide sense stationary?

Which is the best definition of a weak sense stationary process?

Weak-Sense Stationary Processes: Here, we define one of the most common forms of stationarity that is widely used in practice. A random process is called weak-sense stationary or wide-sense stationary (WSS) if its mean function and its correlation function do not change by shifts in time.

What is the difference between wide sense and strict sense?

The process is SSS (strict-sense stationary) if its N t h order probability density function is stationary for any given N. The process is WSS (wide/weak-sense-stationary) if its mean value is constant μ x (t) = μ x, and its autocorrelation function depends on time difference between 2 samples, R x (t 1, t 2) = R x (τ).