An audio signal s(t) is normalized, whose Fourier transform S(f) is shown in the figure, so that |s(t)| ≤ 1. This signal is to be transmitted using FM with a frequency deviation constant k_f = 90 kHz/V. What is the bandwidth required for transmission of the FM audio signal?

The correct option is 3

Concept:

According to Carson's rule signal, BW is given as:

B.W = (β + 1) 2fm

\(\becauseβ=\frac{Δf}{f_m} \)

B.W. = 2[Δf + fm]         

If multiple frequencies are available in modulating the signal then,

B.W. = 2(β + 1) fmax 

Calculation:

\(\beta =\frac{K_f \times A_m}{f_m} =\frac{90 \times 10^3 \times 1}{20 \times 10^3}=4.5\)

BW = 2(β + 1) fmax  = 2 x 5.5 x 20 = 220 kHz.

Here, option 3 is correct.