Consider the 2D signal below
I would like to find the changepoints in the signal (using a hierarchical approach). Based on our visual observation, we can see there are 2 main changepoints where the signal 'starts' and 'stops' and we could argue there is potentially another one where the red starts to come in. We could continue to look in more and more granularity if we so wished.
My question is, how could we get a computer to detect these automatically. My intuition from the way I did it was to do as follows:
- Select the first point as our starting point.
- Move along the time axis with another point, finding the Fourier transform of the data between the first point and this point.
- As long as the transformed signal is not become too much more complex (in the information sense), we know that we have not hit any big change.
- Once the signal starts to become more complex (above some threshold level), we select this as our new starting point and repeat.
After this process is finished we now have selected an array of points where our signal changes drastically w.r.t. its spectral make up.
My question then is:
- Does this make sense?
- What metric should I use for the complexity of the Fourier transform?
- Has this already been tackled successfully and if so any references?