Find the Fourier Transform of: a. x(t) = d/dt[(exp(-3t)u(t)) * (exp(-2t)u(t-2))] b. x(t) = 1/(1+jt) Note: In a., the * denotes convolution. Please show full working and no need to solve from definition, using Fourier TF pairs is fine.
Added by Rachel C.
Step 1
We can use the Fourier transform pair: f(t) = exp(-a|t|) <--> F(jω) = 2a/(a^2 + ω^2) to find the Fourier transform of x(t): X(jω) = F{x(t)} = 1/(1+jt) = exp(-jωt)/(1+jω) Using the substitution a=1, we can see that this is the same as the Fourier transform Show more…
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