What does Wide Sense Stationary (WSS) mean?

[@lawrencecohen1619]

Probably the clearest and best explanation of wide sense stationary I have seen to date.

[@iain_explains]

I'm glad you liked it.

[@chloechong940]

to me, it definitely is the clearest and best explanation on WSS

[@skysummer1586]

Thank you for explaining WSS! really needed it as it is difficult to find a proper explanation for WSS

[@iain_explains]

Glad it was helpful!

[@ggh4627]

In noise cancelling system, because the dusturbance noise including our voice is non stationary, we update the filter coefficient right? who say to me that in airpod and sony headset that use ANC they not use adaptive filter. filter is fixed. the question is in the ANC earbud and headset, they use adaptive filter? and the noise that we want to cancel is non-stationary signal?

[@soumyaneogy9522]

Thanks for this video . The explanation was very clear .

[@iain_explains]

Glad it was helpful!

[@luuknoordam]

Thanks for the video!

[@iain_explains]

You're welcome!

[@BoutinMathieu]

When you say "finite order distributions", do you instead mean "finite order moments" (at time 1:51) ?

[@iain_explains]

Yes.

[@Physalus]

Sir, thanks a lot.

[@iain_explains]

You're welcome. I'm glad it helped.

[@MrKingoverall]

I LOVE YOU MAN !!!!!!!!!!!!

[@iain_explains]

Thanks so much. I'm glad you are finding the videos helpful.

[@PE-gw5gu]

Thanks sir🌹🌹🌹🌹

[@iain_explains]

Most welcome

[@tykilee9683]

Thanks a lot!!

[@iain_explains]

You're welcome!

[@science_engineering]

Does the second moment has to stay the same for WSS too?

[@iain_explains]

Yes. Since the autocorrelation function is only a function of the time difference, and not the absolute times, then for a time difference equal to zero, you get the same value of R_X(0) = E[X^2] no matter what the time is.

[@science_engineering]

@@iain_explains , TY

[@chrisjfox8715]

Thanks for the explanation! What's not quite making sense to me is how mean could be a function of time to begin with. If you're assessing the mean at a particular point in time then are you looking at the mean of all X values up to that time point, or are you looking at the mean of all X values within some window centered at that time point? And if it's the latter, then who's to say what the time-width of that window is (considering how wide or narrow it is could be the very thing that determines just how time-invariant the mean is)? OR, when you say the mean of the function X(t) at some particular time, say t=t_i, is it in reference to X(t) being a Random Process (i.e., multiple instances of the X(t) signal are averaged at each value of t...and WSS is met when the mean X(t=t_i) is constant for each and every value of t_i)? If this is the case, then wouldn't it make more sense to think of this mean as a limit (i.e., the mean of X(t=t_i) tends towards a constant value as more and more X_n are included in the average)? And what do we say if for instance only 1 value of X(t=t_i) has a non-constant mean while all other t values have constant X(t=t_i)? Thanks... :)

[@chrisjfox8715]

And under what circumstances would Rx(0) ever NOT be equal to 1?

[@iain_explains]

It sounds like you are getting confused between the "ensemble expectation/mean" (ie. E[.]) and the "time average". It's a very common confusion. I tried to explain it in the following video, but maybe I should make more videos on this conceptual topic: "Expectation of a Random Variable Equation Explained" kzbin.info/www/bejne/aWSXi4qqZ52VlZI