Transient analysis of data-normalized adaptive filters

Tareq Y. Al-Naffouri*, Ali H. Sayed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

126 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)639-652
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2003

Bibliographical note

Funding 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
  • Energy-conservation
  • Feedback analysis
  • Mean-square-error
  • Stability
  • Steady-state analysis
  • Transient analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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