A communication system transmits one of four equally-likely messages defined by: S(t) = 4 cos(27ft)+3 cos(27ft) S(t)=7cos(2ft)+6os(2ft) S(t)=6cos(27f1) + cos(27ft) S.(t)=9cos(2nft) + 4 cos(2ft) Signal duration =T=2Sec f =125.125Hz f =225.125Hz 1. Define the used basis functions. 2. Express the four signals in terms of the defined basis functions. 3. Sketch to scale the signals in S.S and define the D.Bs & D.Rs. 4. Calculate the average transmitted energy. 5. Find an equivalent set of messages with the same probability of error but with minimum energy and calculate the minimum average energy. 6. Define new basis functions to be used, such that their directions are the same as the D.Bs and then express the four signals in terms of the new basis functions.