Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

Find the Fourier transform +00 F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use that +00 1 exp(iox")dx =exp (iOE

write the function y=2sin(x) as a phase shift of y=2cos(x)

What is the Fourier Transform of sinc(2*x) ? Please show your work. I'm so confused

The function f(x) is defined by f(x) = 0 1- |×| for |x|≤ 2 for |x| > 2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = L sin² k k2 dk = π. 0, to show (1)