# Calculating information loss in a signal after smoothing?

I have a signal. I applied Gaussian smoothing to it and then for baseline reduction I appied Tophat filter to the smoothed version.

This is the original signal:

This is the final signal:

I read that KL Divergence helps in finding the information loss between two signals but then again a condition was that the elements of the two distributions must be 1 i.e. There are two distributions P & Q then Pi + Qi = 1.

So is there any other way by which I can do that ?

• The only conditions on P and Q in the KL divergence is that Q must dominate P in the probability simplex over the space the distributions are defined on. There is no requirement that the elements sum to a constant (aside from the sum over P is 1 and the sum over Q is 1).. – Tom Kealy Oct 14 '13 at 15:12