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Homework Statement
f'(p) is the Fourier transform of f(x). Show that the Fourier transform of e^(ip0x)f(x) is f'(p - p0). (using f'(p) for transform)
Homework Equations
f(x) = 1/√(2pi) ∫e^(ipx) f'(p) dp (intergral from -∞ to ∞)
f'(p) = 1/√(2pi) ∫e^(-ipx) f(x) dx (also from -∞ to ∞)
The Attempt at a Solution
So I substituted e^(ip0x) f(x) into the f'(p) formula and after rearranging came up with:
f'(p) = 1/√(2pi) ∫ e^(ix(p - p0))f(x) dx
If I'm completely honest I'm not really sure what I am doing here. I can see that this looks similar to the formula for f'(p) but I was just jiggling things around to see what happened. Its worth mentioning as well that this is a 5 mark question on a past exam paper so I assume that I have to do a lot more than what I have already done. Any advice would be hugely appreciated. Cheers
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