Are all WSS processes first order stationary?

Are all WSS processes first order stationary?

– All stationary random processes are WSS. A WSS process is not always strictly stationary. RX(0) thus is always positive. If a Gaussian process is WSS, then it is also strictly stationary.

What is a wide sense stationary WSS 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 Gaussian wide sense stationary?

An important property of normal random processes is that wide-sense stationarity and strict-sense stationarity are equivalent for these processes. Theorem Consider the Gaussian random processes {X(t),t∈R}. If X(t) is WSS, then X(t) is a stationary process.

What is the difference between wide sense and strict sense stationary?

“Strict sense” stationarity is a strict definition. A “wide sense” SP is “stationary enough” for your practical purposes. It’s kind of like a first order estimate. Maybe a higher order fit is more precise, but it could create so much needless complexity.

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

Are there any WSS processes that are SSS?

Important: Remember that all SSS processes are also WSS, but NOT all WSS processes are SSS.There is only one exception: “Jointly Gaussian Processes”. Jointly Gaussian processes have any order of probability density functions (property of SSS).

How are jointly Gaussian processes related to SSS?

Jointly Gaussian processes have any order of probability density functions (property of SSS). So, even if a jointly gaussian is WSS it is also SSS.And also remember that white gaussian noise process is a jointly gaussian process with 0 mean. So it is WSS and also SSS.