This question asks for the bandwidth of a frequency-modulation (FM) signal according to Carson's Rule. A key feature of FM is that it is theoretically an infinite-bandwidth signal — the modulation process generates an infinite number of sidebands spaced at multiples of the modulating frequency around the carrier. In practice, however, the amplitudes of sidebands far from the carrier become negligibly small, so an effective finite bandwidth is defined that contains essentially all the significant power.

Carson's Rule gives this practical estimate:

B_T = 2(Δf + f_m)

• Δf = peak frequency deviation (how far the instantaneous carrier frequency swings from its center value)
• f_m = highest modulating (message) frequency

This means the bandwidth is twice the sum of the frequency deviation and the highest modulating frequency — the correct option. The rule captures approximately 98% of the total FM signal power within B_T. An equivalent form is B_T = 2f_m(β + 1), where β = Δf / f_m is the modulation index; substituting β back in reproduces the same expression.

Why the other options are wrong:

• Infinite: while FM is strictly infinite in the mathematical sense, Carson's Rule exists precisely to give a usable finite approximation, so "infinite" is not what the rule states.
• Equal to the carrier frequency and twice the carrier frequency: the FM bandwidth depends on the deviation and the modulating frequency, not on the carrier frequency. The carrier merely locates the signal in the spectrum; it does not set the bandwidth.