Dividing two non-noisy signals by each other increases noise

I am doing some signal processing on spectrum data. A methodology I am following requires a ratio of a measured signal S and a reference signal R.

Both of these signals are quite clean but since both have a little noise centered around zero, the quantity S/R becomes very noisy.

I have tried filtering using many methods to no avail.

• The question is a bit vague so would be hard to answer I think. It would be helpful if you could provide more specific details about the specific methodology you are following and expected versus actual result. Jun 25 '21 at 13:51
• Especially if you're not 100% sure on how to answer Dan's question, it might be very very helpful if you could provide us with information why you need this ratio - one of the things DSP algorithm developers very consistently try to avoid is the division by things that get close to zero, so maybe we have a solution to the underlying problem, too! Jun 25 '21 at 14:32
• Maybe a small epsilon term: S / (R + 1e-5), but if R is both signs then S / (sign(R) * (abs(R) + 1e-5)). Jun 25 '21 at 14:36
• I have tried using the epsilon term and it worked!
– Ryan
Jul 8 '21 at 11:14