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Practical results

We have applied our method to two acoustic time series, a single saxophone tone, consisting of 16000 samples sampled at 32kHz and a speech signal of the word mannagif. The latter time series consists of 23000 samples with a sampling rate of 44.1kHz. Both time series have been normalized to stay within the interval . The estimation of the dimension of the underlying attractors yields a dimension of about 2-3 in both cases.

We chose the control input to be linear increasing from to . Stable models we found for both time series using . Namely for the parameter TT we observed considerable impact on the model quality. While smaller TT results in better one step ahead prediction, the iterated model often becomes unstable. This might be explained by the decrease in variation within the prediction hyperplane, that has to be learned. For small TT the model tends to become linear and does not capture the nonlinear characteristics of the system. Therefore the iteration of those models failed.
To large values of TT results in an insufficient one step ahead prediction error, which pushes the model far away from the attractor also producing unstable behavior.





Axel Roebel
Thu Nov 9 12:55:11 MET 1995