How often do problems arise that let you use adaptive filters? Unless I am understanding something incorrectly it seems the requirement that the input signal be stationary(or even WSS) is too strong for most places I would want to use adaptive filters.

Am I wrong? How often do adaptive filters come up in communications and control?

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    $\begingroup$ "how often" is a pretty ... subjective matter. I'd answer "pretty often"; and you'd be none the wiser, would you? So, let's concentrate on the other question, right? $\endgroup$ – Marcus Müller Oct 4 '18 at 0:35
  • $\begingroup$ Why do you believe an adaptive filter cannot be successfully used unless the input is stationary or WSS? Adaptive filters are used often and come up very frequently in communications and control. $\endgroup$ – Dan Boschen Oct 4 '18 at 3:14
  • $\begingroup$ Ill echo Dan and Marcus and say these filters are widely applied in a variety of fields, and how often they’re used depends on the systems in question. True, some sense of stationarity is needed to achieve a desired solution, but WHERE that stationarity occurs is key. A lot of systems assume a local stationary within some number of samples and take a block approach, where the signal is cut up into blocks and processed separately. The block approach is both computationally efficient, and usually works reasonably well for a good chunk of problems (radar, communications, etc). $\endgroup$ – matthewjpollard Oct 4 '18 at 5:59
  • $\begingroup$ I'd also add that WSS (which is weaker than "stationary", which typically means "strong sense") isn't such an abhorrent requirement: Anything that actually has a PSD is WSS, and if e.g. your channel doesn't fulfill that requirement, then you get into a whole class of different problems (which you can usually only solve by your comms happening so slowly that the first central moments become sufficient to describe the channel, i.e. your symbols become significantly larger than the channel's coherence time (which then becomes hard to define, but ... rabbit hole), so that you can "average it out") $\endgroup$ – Marcus Müller Oct 4 '18 at 6:22
  • $\begingroup$ Most signals of interest don't have a constant mean, which is an example of what I'm talking about. $\endgroup$ – FourierFlux Oct 6 '18 at 20:05