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Help finding ths Fourier transform
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[QUOTE="gony rosenman, post: 6077141, member: 644934"] [h2]Homework Statement [/h2] find the Fourier transform of the following function in [U]two ways [/U], once using direct computation , and second using the convolution therom . [h2]Homework Equations[/h2] [IMG]https://photos.app.goo.gl/JTbfgV4bPmqUm6G66[/IMG] [IMG]https://photos.app.goo.gl/JTbfgV4bPmqUm6G66[/IMG]Acos(w[SUB]0[/SUB]t)/(d[SUP]2[/SUP]+t[SUP]2[/SUP]) [h2]The Attempt at a Solution[/h2] I tried first to solve directly . used Euler's identity and got ∫e[SUP]-it(w[SUB]0[/SUB]+w)[/SUP]/(d[SUP]2[/SUP]+t[SUP]2[/SUP]) + ∫e[SUP]it(w[SUB]0[/SUB]-w)[/SUP]/(d[SUP]2[/SUP]+t[SUP]2[/SUP]) but I think it was a deadend , unsolvable integral . I got a hint from an internet source saying to use the Lorentzian transform but I am not familiar with it then I tried going first from the convolution approach , which means I find the separate F transform of cos(w[SUB][SUB]0[/SUB][/SUB]t) and of 1/(d[SUP]2[/SUP]+t[SUP]2[/SUP]) and then calculate the convolution of them in order to get the FT of the multiplication oh them . I couldn't do that as well because I didn't manage to integrate e[SUP]-iwt[/SUP]/(d[SUP]2[/SUP]+t[SUP]2[/SUP]) and so can't find that Fourier transform as well any direction ,or explained hint would be greatly appreciated! [/QUOTE]
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Help finding ths Fourier transform
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