Question 6 Define the function f(t) by where k > 0 is a real number. f(t) = {e+tt, Je-kt, t≥0 0, otherwise (a) Sketch f(t) and find its Fourier transform (F.T.). (b) Calculate the F.T. of df/dt in two ways: (i) by differentiating f(t) and then finding the F.T. of the result; and (ii) using the F.T. differentiation property. (c) Sketch g(t) = f(t)f(-t) and, using the time scaling and linearity properties, or otherwise, find the F.T. of g(t).