Calculating elements of A from k-point mean values

I have data only of a weighted moving average.

ex_M = [1 2 1 2 2 2 3 4 3 4 4 6 ];

The values were calculated from a five second windows, at one minute intervals. Is there a way to infer what the actual data points are at each five second interval? I realize this would be estimations and not exact values.

I believe this would be the opposite function of: M = movmean(A,k).

Or is there another function in Matlab that can perform something similar? Any help would be appreciated.

Thanks

Answer 1

[Image Analyst]

You can get the original signal only if you know the weights. Otherwise with unknown weights and unknown original signal, there is an infinite number of combinations that could give you that vector. This is called an "inverse filter". There's a ton of information on the web about inverse filters, so do a web search.