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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?

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  • \$\begingroup\$ You rather ask this question in the signal processing forum, you will probably have better answer \$\endgroup\$ – M.Ferru Jun 12 '17 at 12:00
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This document entitled Frequency Modulation (FM) Tutorial by Lawrence Der, Ph.D. of Silicon Laboratories Inc. shows that: -

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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: -

enter image description here

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.

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

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