Consider the multi- tone FM signal shown below:
$s (t) = A_{c} c o s [2 π f_{c} t + β_{1} s i n (2 π f_{1} t) + β_{2} s i n (2 π f_{2} t)] V$
$H e r e, f_{c} = 1000 k H x, f_{1} = 15 k H z a n d f_{2} = 10 k H z .$
The frequency gap between any two immediately adjacent side- band components(either on upperside or on lower side from $f_{c}$ ) in the spectrum of the signal s(t) is

10 kHz

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15 kHz

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5 kHz

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25 kHz

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Solution

The correct option is C 5 kHz
For the given multi- tone signal, the side- band components exits at, $f_{c} + m f_{1}, f_{c} + n f_{2}, f_{c} + (m f_{1} + n f_{2})$
where m and n are integres vary from $- \infty t o + \infty$ .
$G i v e n t h a t, f_{c} = 1000 k H z, f_{1} = 15 k H z a n d f_{2} = 10 k H z$
$f_{c} + m f_{1} \Rightarrow 1010 k H z, 1030 k H z, 1045 k H z . . . . .$
$\Rightarrow 985 k H z, 970 k H z, 955 k H z . . . . .$
$f_{c} + m f_{1} \Rightarrow 1010 k H z, 1020 k H z, 1030 k H z, . . .$
$\Rightarrow 990 k H z, 980 k H z, 970 k H z . . . . .$
$f_{c} + n f_{2} \to 1005 k H z, 1020 k H z, 1025 k H z, 1035 k H z 1040 k H z, . . . .$
995 kHz, 980 kHz., 975 kHz, 965 kHz, 960 kHz, ....

If we plot all these components on a single axis, we get frequency components such that the adjecent sideband frequencies are separated by 5 kHz.

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Consider the multi- tone FM signal shown below: s(t)=Accos[2πfct+β1 sin(2πf1t)+β2sin(2πf2t)]V Here, fc=1000kHx, f1=15kHzand f2=10kHz. The frequency gap between any two immediately adjacent side- band components(either on upperside or on lower side from fc) in the spectrum of the signal s(t) is