If one takes the autocorrelation of a stationary signal, and then that of a non-stationary signal, then would it be possible to say which one is stationary from the ACFs?
Hello,
Let x(t) be a random process with correlation:
Rxx(Ti,Tj) = E{x(Ti) x(Tj)^H}
where Ti and Tj are two different time instants
E{.} is the expectation or average.
H is the hermitian operator.
Then x(t) is said to be stationary (or wide sense stationary) if Rxx depends only on Ti-Tj
meaning that Rxx is a function of the lag difference only and not on the instance Ti and Tj.
So to answer your question, you should choose
Ti-Tj = some constant (say 1) in your simulations and plot the ACF over several values of Ti and Tj ( for example Ti = 3 and Tj = 2 and then Ti = 4 and Tj = 3 and then Ti=5 and Tj = 4 and so on.....). If you observe that ACF is invariant given Ti-Tj = 1 and your tuning these values of Ti and Tj then your signal is stationary.
If your ACF is changing from one (Ti,Tj) point to another provided Ti-Tj = constant then your signal is non stationary.
Hope this helps
Hello,
Let x(t) be a random process with correlation:
Rxx(Ti,Tj) = E{x(Ti) x(Tj)^H}
where Ti and Tj are two different time instants
E{.} is the expectation or average.
H is the hermitian operator.
Then x(t) is said to be stationary (or wide sense stationary) if Rxx depends only on Ti-Tj
meaning that Rxx is a function of the lag difference only and not on the instance Ti and Tj.
So to answer your question, you should choose
Ti-Tj = some constant (say 1) in your simulations and plot the ACF over several values of Ti and Tj ( for example Ti = 3 and Tj = 2 and then Ti = 4 and Tj = 3 and then Ti=5 and Tj = 4 and so on.....). If you observe that ACF is invariant given Ti-Tj = 1 and your tuning these values of Ti and Tj then your signal is stationary.
If your ACF is changing from one (Ti,Tj) point to another provided Ti-Tj = constant then your signal is non stationary.
Hope this helps
Dear Laya Das,
Ahmad Bazzi has explained very well. Further, You can use MATLAB functions for simulating correlation and auto-correlation of signals,
Indeed, Ahmad Bazzi has answered very well. Change in autocorrelation is thus used to detect "critical slowing down" in systems approaching a regime shift.
Such simple explanation looks OK, but for random signals it is very important to know what kind of non stationary situation you have. Phase nonstationarity and amplitude nonstationarity can give absolutely different results performing correlation analysis
- Badges
- Science topic
- Similar topics
- Engineering
- Electrical Engineering
- Signal Processing