2.31. Without actually computing them, but using appro- priate sketches, tell if the Fourier transforms of the signals given below are real, imaginary, or neither; even, odd, or neither. Give your reasoning in each case. (a) x₁ (t) = II (t + 1/2) - II (t-1/2) (b) x2(t)=II (1/2) + II (1) (c) x3 (1)=sin (2) II (1) (d) x4 (1)=sin(2x+л/4)ПI (1) (e) x (1)= cos (2лt) II (t) (f) x (1)=1/[1+(1/5)]