Fourier transform problems
1. A continuous time signal x(t) has the Fourier transform X(ω) = 1/(jω+b) where b is a constant. Determine the Fourier transform for v(t) = t^2 x(t).
2. A continuous time signal x(t) has the Fourier transform X(ω) = 1/(jω+b) where b is a constant. Determine the Fourier transform for v(t) = x(t) * x(t).
3. Compute the Fourier transform for x(t) = te^-t u(t)
4. Compute the inverse Fourier transform for X(ω) = cos 4ω.
5. A signal with the highest frequency component at 10 kHz is to be sampled. To reconstruct the signal, the sampling must be done at a minimum frequency of?