In digital communications, we use a 2-dimensional signal space to describe the setof possible transmitted signals. The basis functions are \phi_{1}(t)=\cos \left(2 \pi f_{c} t\right), \quad 0 \leq t \leq T \phi_{2}(t)=\sin \left(2 \pi f_{c} t\right), \quad 0 \leq t \leq T where fc is the carrier frequency and T is the time length of the signal. a) Show that these signals asymptotically orthogonal. That is, show that they are orthogonal if f.TC » 1.are ) If the signal error probability is pe(d) = e-a, where d is the distance betweenthe signals, find the error probability for the signals described in part (c).-5d

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