Inverse Fourier Transform and Power Signals

[mod31489]

I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem:

Question: Given the Fourier transform of an aperiodic signal

X(ω) = 2*sin(3(ω-2π))/ω-2π

(a)find its inverse Fourier transform x(t) using only tables and properties
(b) find the power of the signal x(t)


I know that I have to preform Frequency shift property involving the 2π and I have to preform the scaling property for the 3. I also know that I can use the relationship

sin(τω)/ω = τsinc(τω/2)

and the inverse Fourier transform of
τsinc(τω/2) → ∏(t/τ)

The problem I am having is understanding how to perform the frequency shift and the scaling property in order to get X(ω) into the form of sin(τω)/ω so i can preform the inverse Fourier transform. from there the power is equal to x^2(t) which is equal to the

lim T→∞ of ∫ g^2(t)dt from -T/2 to T/2

 

[aralbrec]

Question: Given the Fourier transform of an aperiodic signal

X(ω) = 2*sin(3(ω-2π))/ω-2π

The problem I am having is understanding how to perform the frequency shift and the scaling property in order to get X(ω) into the form of sin(τω)/ω so i can preform the inverse Fourier transform.

You should look at replacing w with something else so that X(w+?) generates the sin(ax)/x term.

The signal is not periodic so I think you misspoke -- it doesn't make sense to speak about power for aperiodic signals so I think you meant energy. Subtle, I know, but it's important to keep it straight :)