Problem 2: 2.4 (a) Consider two signals of duration 7 seconds: 40(1) = 91(1) = 40(1) = √√COS(2 √cos(2 91(1) = Determine the minimum separation between fo and f₁ so that

po(t) and 4₁ (t) are orthogonal. You may assume that (fo + fi)T » 1. (b) Consider two signals of duration Ţ seconds: √ cos(2лfot)pr(t) √ cos(2лfit)pr(t). cos(2л fot)pr (1) sin(2л fit)pr(t). Determine the minimum (nonzero) separation between fo and f₁ so that yo(t) and ₁(1) are orthogonal. You may assume that (fo+fi)T » 1./n(c) Consider two sets of orthogonal signals of duration 7 seconds. Signal set one consists of signals po(t) and ₁(1): 40(t) = 91(1): Signal set two consists of signals o(t) and ₁(1): 40(t) = cos(2л fot) pr (t) √ 4/1(1): sin(2л fot)pr (t). cos(2л fit)pr (1) √ sin(2лf₁t)pr(t). Determine the minimum separation between fo and f₁ so that either signal in signal set 1 is orthogonal to any signal in signal set 2. You may assume that (fo + fi)T » 1.