Quote from jacksmith:
How about these adaptive filter in communication ?
Wireless channel is not stationary, but people have built communication theory for it.
adaptive filters are used primarily as equalizers (matched filters) to provide the detector with optimal signal to noise ratio.
The tap weights of the filter adapt in real time to provide the "inverse" of the band-limited channel to the extent the length of the filter allows. It's usually an accuracy vs. hardware efficiency tradeoff.
From my days in engineering, the key assumption that facilitates system design is that the system will be 1) linear, and 2) time-invariant. 2) is relevant in this case. Without time time-invariance, the frequency response of the channel will be constantly drifting, and the filter will never adapt to a stable matched configuration. The signal detection will be absolutely crummy, even when sophisticated coding has been applied to the signal.
In wireless, the channel is not isolated, as is the case with certain other applications. Problems such as high-power interferers, adjacent to the small, desired signal in the spectrum pose "receiver sensitivity" challenges. In addition, cellular receivers face the problem of multipath, where a radio signal can propagate through multiple geometric paths, resulting in time-delayed echoes on the receiver-side. However, these application-specific challenges never change the fact that a transmitted radio signal is ALWAYS received as a sinusoid, and the spectral characteristics of wireless channels are well-known.
This is NOT the case of financial time series, where the power spectrum is constantly shifting in time due to changes in volatility, drift value, and also, very importantly, poisson events.
rt