Nonlinear System Identification by Haar Wavelets by Przemysław Śliwiński

Author:Przemysław Śliwiński
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5.29)

with the empirical coefficients computed as10

Each set , being a subset of the set of all wavelet empirical coefficients, contains translation indices corresponding to the empirical coefficients at the scales , which are created by the EZW algorithm and are (tentatively) located in the cones of influences of the jumps; see Sect. 6.3 for implementation of the EZW.

5.5.1 Convergence and Convergence Rates

The following pair of theorems describes the algorithm convergence conditions and the best- and worst-case convergence rates. The first is the counterpart of Theorem 5.5.

Theorem 5.11.

If the scale of the estimate in (5.29) and the empirical cone number are selected so that

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