Given the following signals, suppose that all energy spectral components outside the bandwidth |f| ≤ W  are removed by an ideal filter, while all energy spectral components within this bandwidth are kept. Find the ratio of energy kept to total energy in each case. (α, β, and τ are positive constants.)

(a) x₁ (t) = e ^-αtu(t) 

(b) x₂ (t) = II (t/τ) (requires numerical integration)

(c) x₃ (t) = e^-αtu(t) - e^-βtu(t)