Transient analysis of data-normalized adaptive filters

T. Y. Al-Naffouri and A. H. Sayed, "Transient analysis of data-normalized adaptive filters",  IEEE Transactions on Signal Processing.   vol. 51 , pp. 639-652, Mar 2003.


This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.