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Academic Press Library in Signal Processing by Rama Chellappa, Sergios Theodoridis

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1.12.4 Statistical analysis

Closed-form expressions for the mean-square performance of adaptive filters facilitate comparisons between different algorithms and provide information about stability, convergence rate, mean-square error, and tracking capability. Since adaptive algorithms are obtained from stochastic approximations of the cost-functions, gradients and Hessians, their performance will degrade in comparison with the performance of the exact algorithms. Thus, stochastic analyses are also important to measure the performance degradation in relation to the exact algorithms.

The analysis of an adaptive algorithm constitutes a very hard problem, since adaptive filters are time-variant, stochastic, and nonlinear systems. Therefore, it is ...

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