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Consider a continuous-time signal x(t) given by: x(t)=e⁻ᵗfind the Fourier transform of the signal x(t).

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Final answer:

To find the Fourier transform of the given signal x(t)=e^(-t), substitute the signal into the formula for the Fourier transform and solve for F(w).

Step-by-step explanation:

The Fourier transform of the given continuous-time signal x(t)=e^(-t) can be found using the formula:

F(w) = ∫ x(t)e^(-jwt)dt

Substituting the given signal into the formula:

F(w) = ∫ e^(-t)e^(-jwt)dt

Simplifying the expression:

F(w) = ∫ e^((-1-jw)t)dt

Integrating this expression and solving for F(w) will give the Fourier transform of the signal x(t).

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