Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

Find the Fourier Transform of f(s) = e-αx² α > 0

(b) Find the inverse Fourier transform of the following: (11) 1 √w√2π (3+jw)

(2) Compute the Fourier integral representation for the function f(x) = x² for 0< I< 27.

Please find the Fourier integral representation of the given function

Find the Fourier transform of f(t) = [Aeat ]u(t) and draw the amplitude and phase spectrum

Find the Inverse Fourier Transform of the following functions: (a) F(a): 6+5ia-a2 2 sin a (b) F(a) %3D a(1+a²)

Determine the pole of the following functions and residue at each pole: (a) f(z) = z²-1 z²-5iz-4