3
$\begingroup$

I need to represent my signal as a set of transitions from one level to another, and I am interested in transitions that have relatively big amplitude 2000+.

I applied median filter to get rid of the high frequency part of the signal and result looks like this. Now I can take gradient and get set of transitions, and based on the magnitude of these transitions, keep only big one. So, I will get transition, corresponding to the left side of this peak, I will filter out transitions from the top. But I would like to have right side of this peak also to be represented as one nice 2000+ transition. But as you can see on the picture, there is small kink in the middle of the right side that will break my transition into 2 parts.

Is there some kind of a filter that will transform my signal and remove this kink?

enter image description here

$\endgroup$
  • $\begingroup$ yes there are such algorithms $\endgroup$ – Fat32 Jan 7 '16 at 23:49
1
$\begingroup$

One of many possible algorithms to provide such edge sensitive information to its users are classified under change-detectors. The one that best fits to your kind of data uses thresholds, accumulators, memory, leakage and smoothing factors as well as variance and mean normalizers to decide on which changes belong to meaningful edges and which are just local variations.

$\endgroup$
  • $\begingroup$ Could you please share link to paper, book, keywords that I can use to google, something else that may lead to an example of such algorithms ? $\endgroup$ – Vladimir Jan 8 '16 at 17:26
  • $\begingroup$ Adaptive Filtering and Change Detection_GUSTAFSSON_WILEY is enough for a beginner. $\endgroup$ – Fat32 Jan 8 '16 at 19:19
1
$\begingroup$

The small kink is something a larger median filter could have removed, and that a discrete derivative finer than a gradient could have smoothed.

So instead of using a nonlinear median, then a derivation operator, you could combine them with a weighted median filter, having both positive and negative weights. This could yield a sort of "median gradient", that could be more robust to kinks.

The basic theory is exposed in another answer to What is the advantage of weighted median filter over median filter?, with more details in the paper A General Weighted Median Filter Structure Admitting Negative Weights, Arce, 1998.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.