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https://en.wikipedia.org/wiki/Lulu_smoothing

I'm interested in using this approach to remove signal spikes from an analog sensor connected to a microcontroller. I understand the L and U operations, however the Wikipedia page fails to indicate how these two results would be combined.

Is the resulting dataset from L fed into U (or vise versa for UL). IE L(U(dataset))?

Cody Smith
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    Going by the figures in Wikipedia's "Examples" section, LU means apply L then U, i.e. U(L(data)). However according to Conradie et al. (2006) it means the opposite. I didn't check the other references. –  Apr 21 '17 at 20:39
  • The article states "The Lulu smoothers are composed of repeated applications of the L (lower) and U (Upper) operators". I guess it is up to the user to decide on the order and number of successive applications of L and U. – Stelios Apr 21 '17 at 20:45

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Rohwer's original paper, "Idempotent one-sided approximation of median smoothers" (1989), appears to be available online as open access. It applies operators on the left, so $L_nU_nx$ means apply $U_n$ to the sequence $x$ and then apply $L_n$ to the result.

(The figures on Wikipedia are inconsistent with Rohwer's notation.)