Given the following functions of : R x1 () = 4 exp(-||) cos 2 R x2 ()

Given the following functions of τ:

R_x1(τ) = 4 exp(-α|τ|) cos 2πτ

R_x2(τ) = 2 exp(-α|τ|) + 4 cos 2πbτ

R_x3 (f) = 5 exp(-4τ²)

(a) Sketch each function and fully dimension.
(b) Find the Fourier transforms of each and sketch. With the information of part (a) and the Fourier transforms justify that each is suitable for an auto correlation function.
(c) Determine the value of the dc power, if any, for each one.
(d) Determine the total power for each.
(e) Determine the frequency of the periodic component, if any, for each.