# 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

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.