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The Fourier transform of a signal x(t), denoted by X(jω), is shown in the figure. Let y(t) = x(t) + ejtx(t). The value of Fourier transforms of y(t) evaluated at the angular frequency ω = 0.5 rad/s is

The Fourier transform of a signal x(t), denoted by X(jω), is shown in the figure. Let y(t) = x(t) + ejtx(t). The value of Fourier transforms of y(t) evaluated at the angular frequency ω = 0.5 rad/s is Correct Answer 1.5

y(t) = x(t) + ejtx(t)

x(t) ↔ X(jω)

ejtx(t) ↔ X(j(ω - 1))

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y(jω) at ω = 0.5 rad/sec = X(jω) + X(j(ω - 1))

= 1 + 0.5 = 1.5

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