Final answer:
The Fourier transform of the function x(t) = e^-a|t| is X(ω) = 2a/(a^2+ω^2) where a is a positive constant.
Step-by-step explanation:
The Fourier transform of the function x(t) = e-a|t| is given by X(ω) = 2a/(a2+ω2) where a is a positive constant.
To compute the Fourier transform, we can apply the definition of the Fourier transform. The formula for the Fourier transform of a function f(t) is given by F(ω) = ∫[f(t)e-iωt]dt where ∫ denotes the integral and e is the base of the natural logarithm.
In this case, we have x(t) = e-a|t|, so we can substitute this expression into the formula and integrate over t to compute X(ω).