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I am searching for some strange signals in order to test an algorithm that I am developing. I've found an article by Donoho and Johnstone where they propose to test the algorithms using Blocks, Bumps, Heavysine, and Doppler signals. Is there any other signal that is generally difficult to be estimated? I am not really into this topic and I would really appreciate some help. Thanks in advance.

Edit: As suggested in the comments I'll provide some context. I am working with Spline regression in noisy context. My idea is to provide an alternative solution for the Smoothing Spline by using an adaptive algorithm that chooses the location of the knots according to the behaviour of the data. For instance if I would like to approximate a Doppler signal I would expect the algorithm to put very dense knots on the lefter side to capture the rapid movements and sparse knots in the righter side instead. I've been suggested to ask this in here even though I am not quite sure if it's a suitable question for this particular site.

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    $\begingroup$ It might be useful to know what kind of algorithm you're developing. Signals problematic in one case may be trivial in another. $\endgroup$ – MBaz Feb 13 at 15:17
  • $\begingroup$ I've edited it. $\endgroup$ – RScrlli Feb 13 at 15:25
  • $\begingroup$ I think that you are going to have to specialise this a little further if you are after some useful responses. There are plenty of examples of difficult to estimate signals but how would this inform your decision process? You need to define some criteria about the characteristics of the signal versus its approximation. What conclusion would you make if you were presented with an impossible to approximate signal? What are you trying to achieve? $\endgroup$ – A_A Feb 15 at 15:04

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