Question

(prove orthogonality only)

8.6 Show that if fi = and f2 = then the energy in each of the signals si(t) and s2(t), given by Equation (8.2.15), is equal to Ep, and furthermore, they are orthogonal. Also show that if the above conditions are not satisfied but fiT » 1 and f2T» 1, then the energy in s0) and s2() can be very closely approximated by Ep, and the inner product of s1(t) and $2(t) is very close to zero. Note that since T, is the duration of the rectangular pulse, 1/Th approximates its bandwidth. Therefore, the conditions fi Th l and f2T 1 mean that the carrier frequencies fi and f2 are much larger than the bandwidth of the rectangular baseband pulse, a condition that is usually satisfied where k and k2 are distinct positive integers, cos 2T fit Th

Answer 1

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