- #1

mod31489

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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