Question 8 (4+1+1+2+2=10 marks): 0 t

Ouestion 8 (4+1+1+2+2=10 marks): O, 1, 1st < 2 Consider the function f (t) = 6, a) Write f (t) in terms of the Heaviside function and find it's Fourier transform. b) What is the Fourier transform of f(5t)? C) What is the Fourier transform off (t 1)? d) Find the Fourier transforms of e'tf(t) and e-itf(t)? e) Find the Fourier transforms off(t)cost andf(t)sin t?