Correct Answer - Option 3 : decreased by one fourth
We have output \(\rm SNR\) of an FM system is:
\(\rm {\left( {\frac{S}{N}} \right)_o} = 3{\left( {\frac{{\Delta f}}{f}} \right)^2}.{S_X}.\gamma\)
where \(\rm \gamma = \frac{{{S_i}}}{{\eta B}}\) is \(\rm SNR\) of baseband system or channel signal to noise ration.
As for baseband \(\rm {S_o} = {S_i}\left( {\therefore \frac{{{S_o}}}{{\eta B}} = \frac{{{S_i}}}{{\eta B}}} \right)\).
Carson's rule: Bandwidth of FM BWFM = 2 [ Δf + fm ].
fm is doubled then, the bandwidth is also doubled and hence according to the relation, we can see that the
SNR is decreased by one fourth.