If X and Y are independent then they are uncorrelated. It is not true, however, that if they are uncorrelated, they must be independent. For example, if X is uniformly distributed on [−1, 1] and Y = X2 then they are uncorrelated even though X determines Y, and Y restricts X to at most two values.
Moreover, uncorrelatedness is a relation between only two random variables, whereas independence can be a relationship between more than two.
Feuer and E. Weinstein, "Convergence analysis of lms filter with uncorrelated gaussian data," IEEE Trans.
The variance of the gain estimate, var(ff) which equals the steady state value of ffl ff (k) is thus given by var(ff) ff oe 2 s (14) It is seen that the value of var(ff) increases with the step size, ff, and the signal power, oe 2 s.
The matrices H(t) and G(t; 1) are also influencing the convergence behavior of the algorithm, and even for the simple case of linear time invariant blur and no motion there are limitations emerging from the ill posedness of the model equations.
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