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- 16. Find the Fourier transform of f(x), show the details. f(x) = |x|e¹x1 (-∞0Find the laplace transform of the piecewise function: S2t y = t2 0Q3) Verify that the Fourier transform of the function [1-x|, |x|1 a. Then Show that 2 sin u sin u b. Compute the integral 2 du sinu u is T 4 4 du sin² 2² (k/2) (4/2)² ƒ(k)=2U. Use the Fourier transform synthesis equation to determine the inverse Fourier transform of: a) X,(e*) = E {2a8(w- 2nk)+ TỔ(w- -- 2 īk) +T8(w+- 5zk)} 3 4 X, (e") = 5j for 0Let f be a function on R with Fourier transform 1 F[f](s) = f(s) = f(x) e** dx. irs (a) Show that the Fourier transform of the function ga(x) : f(ax), where a > 0 is a constant, is Flg.|(6) = Lf (). 1 (b) Show that the Fourier transform of the function Je-, r20 f(x) = 0, x < 0 is f(s) = 1 1+ is V2n s2 +1Sketch for the Fourier transform of f(x)Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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