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This is a question on taking the Fourier transform of a function.

How does one find the fourier transform of $f$, where $f(t) = |t|$?

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See Fourier Transform. Can you follow the derivation? –  Amzoti Dec 23 '12 at 6:07
    
This helps a lot; thanks. I'm surprised that we'd have to deal with derivatives of dirac deltas to solve this problem; I thought it would be simpler than that since it came on a midterm. –  user24205 Dec 23 '12 at 6:14
    
@user24205: without any additional trick you can define the Fourier transform only when $\int dt\,f(t)e^{i\omega t}$ converges. For your example, this integral is diverging as it stands... –  Fabian Dec 23 '12 at 6:21
    
You can check the result using WA –  Amzoti Dec 23 '12 at 6:33
    
It boils down thinking about how use the signum function to express the absolute value and then using the definitions for Fourier Transform. I would go through the example and make sure you can follow the entire derivation. Have fun! –  Amzoti Dec 23 '12 at 6:44
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