Algorithms for finding features in time series (+ example pic)

Beginner to machine learning here. I am looking for a feature-based approach to classify and compare time series data. I have a picture:

http://i.imgur.com/ZAhH8So.png

There are 3 axes of time series data which changes in time. In the purple boxes are examples of 2 data sets which should have the same features (or very similar).

What algorithm(s) should I look into for extracting and comparing features for this sort of data?

Thanks!