Is it possible to find the smoothness ($C^1$, $C^2$,... continuity) of a time sampled signal?
For a continuous function continuity can be found by the number of existing derivatives. When does the derivative for a discrete time signal exist?
Deriving a discrete signal using e.g. finte differences is always possible I guess and therefore I was wondering how to find the continuity of a discrete signal?
In Matlab I thought of using dx = gradient(x) multiple times until I get "large peaks" above a predefined threshold, which would make it possible to define some sort of "pseudo smoothness" for a discrete signal.
Is there a better approach?