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KeithKp
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Homework Statement
By applying Parseval's (Plancherel's) theorem to the function
f(x) = -1 for -2 ≤ x < 0
1 for 0 ≥ x < 2
0 otherwise
determine the value of the following integral.
∫ dk sin^4(k)/(k^2) (Integral between ±infinity)
Homework Equations
Parseval's Theorem, i.e the integral of the modulus squared of a function is equal to the integral of the modulus squared of its Fourier transform.
Fourier Transform formula.
The Attempt at a Solution
I've tried multiple times to try and arrive at the correct answer of pi/2 but I just can't do it. Is the Fourier transform:
∫-dx e^(ikx) + ∫ dx e^(ikx)? (First integral is between -2 and 0, second between 0 and 2). Because I can't get the correct answer doing that.
And for the equation of the function, is it just sgn(x), with the integral between -2 and 2? How else do I write f(x) given those boundaries? If I use sgn(x) between -2 and 2, I get 4 for the left hand side. But I still can't derive that integral.
If someone would just start me off with the correct Fourier transform equation, i'll go away and crunch the integration myself.
Thank you.
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