# 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).. Oct 14 '13 at 15:12

## 2 Answers

Information loss and KL Divergence are functions that describe the behavior of random variables, in other words a set of random signals from some distribution. When you only have one signal, like you do in this case, calculating the information loss doesn't make sense. You can calculate mean squared error like the other comment suggests.

• Indeed. Good you pointed that the KL is "Distance" between distributions and not between signals.
– Royi
Jun 30 '18 at 14:13

For measuring the difference between a signal and an estimation/modification of that signal I usually just take the Mean Square Error or Root Mean Square Error. It is simple to calculate and provides a single metric to describe how far your signal deviates (or technically, variates) from the original.