# Relation between Signal to Noise Ratio (SNR) and Transmission Bandwidth for FM signal

I was encountered by the below question ::

The transmission bandwidth (BW) is doubled in an FM(Frequency Modulated) signal. So, the resultant SNR (Signal to Noise ratio is) ?

The answer is given as doubled - SNR is directly proportional to (BW)^2

How can we prove this?

• You rather ask this question in the signal processing forum, you will probably have better answer – M.Ferru Jun 12 '17 at 12:00

## 1 Answer

This document entitled Frequency Modulation (FM) Tutorial by Lawrence Der, Ph.D. of Silicon Laboratories Inc. shows that: - What the above is saying is that if FM deviation doubled (transmission band width doubled), SNR would increase 8 times. See also this from wiki: - In your question there has to be some form of error because if SNR is "directly proportional to BW$^2$" and BW doubles then SNR must rise by 4.

How can we prove this?

Basically, you can't prove something that is wrong without lying or some form of deception.

• Lying, some form of deception, or starting from different assumptions. – The Photon Jun 12 '17 at 14:40