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An amplitude-modulated signal is written as x_AM(t) = 100 [p(t) + 0.5g(t)] cos(ω_c t) for 0 ≤ t ≤ 1. Which pair can represent the modulating signal and the modulation index?

1. t, 0.5
2. t, 1.5
3. t, 1.0
4. t², 2.0

Correct answer: t, 0.5

Solution

The correct option identifies the modulating signal as p(t) = t and the modulation index as 0.5, which aligns with the structure of the amplitude-modulated signal where the modulation index is defined as the ratio of the peak amplitude of the modulating signal to the carrier amplitude.

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