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.