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The two techniques presented above solved only partly the problem of
determining the delay time and none of it addressed the virulent
problem of noise. Therefore we now turn to the *singular system
analysis* [7] which shows a way how to determine the embedding
dimension and the delay time reliably even in the presence of noise.
We proceed in three steps: In the first step (in section 3.4.1), we
discuss a method to derive a suitable embedding dimension from a
finite data set which is measured with infinite precision. Then, in
section 3.4.2, we generalize the result of the first step to noisy data.
The third step (in the second part of section 3.4.2) gives a slightly
more sophisticated method of construction of the vectors . In section
3.4.3, we again consider the problem of choosing and the
embedding dimension.

**Subsections**

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Martin_Engel
2000-05-25