Inverse fourier transform

[peter.a]

Homework Statement

I can't figure out what the limits of integration should be;

if a transfer function is given as follows:
h(ω)=1 if 1<|ω|<2, 0 otherwise

1) find the impulse response

2) if the input is white noise of intensity σ² find the variance of the output signal

3)state with reasons if the output process is stationary and continuous and differentiable in the mean square sense

Homework Equations

The Attempt at a Solution

 

[Valkarie]

1) the impulse response is h(t)=e^|2-t|-e^|1-t|2) Var(x(t))=σ²∫h²(τ)dτ 3) The output process is stationary as it does not depend on time, and continuous as the impulse response is continuous, however it is not differentiable in the mean square sense as the impulse response has a discontinuity at τ=1 and τ=2.