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.
Bibliographical noteFunding Information:
Manuscript received February 28, 2001; revised October 23, 2002. This work was supported in part by the National Science Foundation under Grants CCR -9732376, ECS-9820765, and CCR -0208573. The work of T. Y. Al-Naffouri was also partially supported by a fellowship from King Fahd University of Petroleum and Minerals, Saudi Arabia. The associate editor coordinating the review of this paper and approving it for publication was Dr. Xiang-Gen Xia.
- Adaptive filter
- Data nonlinearity
- Feedback analysis
- Steady-state analysis
- Transient analysis
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering