2.8 (a) Consider a signal f(t) with unit energy defined over the time interval [0, 7] that is zero outside that time interval. For example, f(t) = √T/Tpr (1). Consider two

signals of duration NT: so(t) = N-1 are orthogonal. Σsouf(t-iT) i-0 N-1 si(t) = Σsuf(t-iT). 132 Determine (so(1), $1(1)) in terms of the sequence Sq, i = 0, 1,...,N-1 and $₁,,i = 0, 1,..., N-1. 1-0 (b) Consider the two signals of duration 27 generated from f(t) and the two vectors so = (+1, +1) and s₁ = (+1,-1). We will form a matrix of vectors. In this case, N = 2: H₂ = 50 51 +1 (39) where the first row can be used to generate a first signal and the second row used to generate a second signal. Using part (a), show that the two signals so(t) = 50,0 f(t)pr (1) + 50,1f(t-T)pr(t-T) $₁(t) = $1,0 f(t)pr(t) + $1,1ƒ(t – T)pr(t – T)