I have data that'ss not too noisy and I am trying to detect a pattern where it gradually increases then decreases in a short period of time (20 ticks? it should be roughly similar per session but can vary slightly between different sessions). This pattern usually happens in pairs but not always.

enter image description here

So looking at the top plot of the data over time, the pattern I am after is at time 100 and 300. you can see the data is roughly stable, then gradually increases and decreases and stabilizes, then after a while again increases, decreases and stabilizes.

As you can see there are also instances where it suddenly changes (550 & 800), or it increases then decreases over a longer period of time (700-800) but I need to detect my short pattern only.

What I have done sofar:

I have taken the variance of the last 10 values which is the middle plot. It gives me a relatively good idea when the data starts to deviate but, variance ignores the sign so I cannot tell if the data is increasing or decreasing and it doesn't differentiate between sudden and gradual changes.

So I decided to take the squared difference between each value and the previous value and keep the sign. I took the square to exaggerate the difference to make it more distinguishable from smaller variations and kept the sign to help identify when it increases then decreases.

I can't say if diff[i] > diff[i-1] for 5 ticks, and then diff[i] < diff[i-1] for 5 ticks because diff is noisy & changes its sign to positive midway at 130 even though overall it was decreasing.

I feel like there would be a better way than trying to filter the noise and then applying that if statement above. But I'm drawing blanks at the moment.

Whats the best way to programatically detect a short but gradual increase then decrease in noisy numbers?


What you need to do is find a feature which separate the phenomenon you're after from the noise.

If the jump is high relative to the noise STD it means it has good SNR when you compare the instantaneous derivative to the noise.

As you figured it out, in the case of great SNR as you shown above it works pretty easily and your approach did the work.

What about cases with bad SNR?
Then you need to apply some pre processing to increase the SNR.
You can apply Low Pass Filter bu it means it will blur the exact location of the "Jump" you're after.
A nice trick I uses once was borrowing from Image Processing a class of filters called Edge Preserving Filters.
For instant it is really easy to apply the Bilateral Filter in 1D.
While it will remove noise and improve the SNR on flat regions it won't hurt the "Jumps" you're after.
So after using it even signals with worse SNR then the example above will start look like the case above and make your current method viable.


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