Theory

A random process is Strict-Sense Stationary (SSS) if its joint probability distribution is constant over time. A process is Wide-Sense Stationary (WSS) if its mean is constant and its autocorrelation function depends only on the time lag (\(\tau\)), not on absolute time.

• WSS Process: Mean is constant. ACF, \(R(t_1, t_2)\), depends only on \(\tau = t_1 - t_2\).
• Non-Stationary (Mean): The mean of the process changes over time.
• Non-Stationary (ACF): The mean may be constant, but the ACF changes depending on where it is calculated in time.

Procedure

• Select a "Mystery Signal" to begin.
• A long realization of the signal will be plotted. Drag the shaded "Inspector Window" across the plot.
• Observe the Local Mean and Local ACF plots. Note how they change (or don't change) as you move the window.
• Once you have a conclusion, select your answer from the dropdown and press "Submit Answer".