4.21. Compute the Fourier transform of each of the following signals:
(a) [e^{-αt} cos ω_0t]u(t), α > 0 (b) e^{-3|t|} sin 2t
(c) x(t) = { 1 + cos πt, |t| ≤ 1; 0, |t| > 1 (d) ∑_{k=0}^{∞} α^k δ(t - kT), |α| < 1
(e) [te^{-2t} sin 4t]u(t) (f) [sin πt / πt][sin 2π(t-1) / π(t-1)]
(g) x(t) as shown in Figure P4.21(a) (h) x(t) as shown in Figure P4.21(b)
(i) x(t) = { 1 - t^2, 0 < t < 1; 0, otherwise (j) ∑_{n=-∞}^{+∞} e^{-|t-2n|}
4.22. Determine the continuous-time signal corresponding to each of the following transforms.