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is there a way we can extract features from a function, and only sample more when we detect the presense of a feature?


Is increasing the sample size the only way that makes the most accurate reconstruction?


Can we do some sort of slightly more complex approximation such as measuring derivative values at each point as well, or is the storage tradeoff generally not worth it?


If you know what the general shape of your signal would be (i.e. sinosudial, logarithmic, polynomial) would you approximate functions of those form at every interval between samples? How much more computationally expensive is this?