I have a signal that is full of noise when I extract its derivatives. Please refer to figure [login to view URL] and [login to view URL]
As you can see, once we differentiate the signal, noise begins to show up, and if I tried to derive the 8th derivative for example, noise will explode.
The Objective here is to derive as many derivatives as we want through reconstruction the original signal without noise so we can differentiate it, or extract the first derivative then smooth it and differentiate then smooth... iteratively.
The key here is that your solution MUST be casual smoothing/filtering, which means that it does NOT induces any delay like digital filter, in other words, Calculating the value of the smoothed/filtered X value doesn't depend on X+1, X+2.....Xn
I've included [login to view URL], which includes the signal along with its derivatives, the first column is the signal and rest of columns are its derivatives (cut from historical data set and the derivatives derived through digital filter, for testing purposes). Your solution MUST be so close to the extracted derivatives in the file
Your solution must be universally solution which means it could be used on any signal of choose.
I prefer the algorithm to be in Matlab but it's not a must.