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I have a bad feeling this is a well explored field I should already know about, but

Say you have some platonic data at given points

...
at 13.0:   1000
at 14.0:   1152
at 15.0:   1000
at 16.0:   1200
...

(of course, the times needn't be regular, but let's carry on)

For any abstract point, you could use the naive strategy of "nearest" point

enter image description here

equally pathetically, make a line between the two around you

enter image description here

What's the technique if you want a smoothish line?

enter image description here

(Obviously, you could adopt different smoothing strategies for different smoothing concepts, but, some solution.)

What's the algorithm in a sense of "let's make some computer code" for this? I'm guessing it's along the lines of weighting with some diminishing number of points around you, but this has surely all been well-considered.

Secondly, is what I am describing here "smoothing a time series" or am I totally offbase?

Thirdly does this have anything to do with RMS or am I offbase?

Fattie
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  • (As described, my tag may be totally incorrect.) – Fattie Aug 15 '19 at 11:37
  • It's not entirely clear what you want exactly from the smoothing. One way of smoothing is to just take the average of the nearest points, for example $$ y_i = \frac{x_{i-1} + x_i + x_{i+1}}{3} $$ You can try this with different amount of smoothing terms and see what the results give. Also, what do you precisely mean with "smooth"? For discontinuous data, it's not very clear what this can mean. – Matti P. Aug 15 '19 at 12:09
  • That seems like an extremely weak approach; it would result in a step-graph (as in image one). Right? – Fattie Aug 15 '19 at 12:12
  • Okay so you mention the bezier curve. What's wrong with using that? I realised now that you're talking about interpolation, and you want the interpolation curves to be nice and smooth. – Matti P. Aug 15 '19 at 12:16
  • Thanks for your interest, let's wait for some experts in (as it says in the title) smoothing and time-series. In the meantime let's clean up completely irrelevant comments, cheers – Fattie Aug 15 '19 at 12:20
  • One approach is to use https://en.wikipedia.org/wiki/Kernel_smoother – them Aug 15 '19 at 13:20
  • Fantastic pointer, @them - thank you so much !!!!!!!! – Fattie Aug 15 '19 at 13:25
  • Ahh .. so "kernel" .. "window function" are key concepts here. – Fattie Aug 15 '19 at 13:27
  • @Fattie this generally falls within the field of nonparametric statistics. Kernel methods are just one approach. https://www.springer.com/gp/book/9780387251455 covers most basics concepts in this field including smoothing kernels (not the best written book, and it comes with a few annoying typos but I think this is a standard textbook for introduction course in nonparametric statistics) – them Aug 15 '19 at 13:31
  • Ahh, "nonparametric statistics" - GOT IT. @them – Fattie Aug 15 '19 at 13:33

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