Fourier Transform of x(t) = ae^(bt)*u(-t)

[Larrytsai]

Hey I am trying to figure out this easy problem, and I don't know if I am doing this properly or not here's the questions & the work.

x(t) = ae^(bt)*u(-t)

F[x(t)] = a*integral[(e^bt)*e^(-jwt)*dt] upper bound = 0 lower bound = -infinity
= [a*e^(t(b-jw))] / (b-jw)
= a/(b-jw)

 

[ideasrule]

What's u(-t), and why is it not part of the Fourier transform? Otherwise, your work is correct.

 

[Larrytsai]

u(-t) is the unit step function with a time reversal.