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Is it when the cost function such as the error signal or Mean Square Error (MSE) signal is minimised?

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  • $\begingroup$ Shooting from the hip i'd say that when you use a fixed step size and your error is of the same scale as your stepsize, then your filter has converged. Depending on how the signal is conditioned, the algorithm used and the stepsize, the filter will end up jumping around the minimum of the error plane a bit. $\endgroup$ – sobek Jan 20 '16 at 19:07
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The adaptive filter is converged when the error is what they call Wide Sense Stationary, meaning the mean and variance of the error are unchanging over long time intervals.

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