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nov 9 - EE 102 Fall 2009 WEDNESDAY NOV 4 09 SIGNALS CHAPTER...

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EE 102 Fall 2009 WEDNESDAY NOV 4 09 SIGNALS : CHAPTER 4 in the Textbook Definition A signal is a real valued function of Time. f H t L , defined over any interval of time such as 0 < t < T, where T can be infinite such that its energy over any finite time interval a < t < b is defined by : Signal Energy = E = a b f H t L 2 t is finite is a finite positive number. . denotes absolute value Signal Power is defined as E T ~~ Time Average for Large T. For example : f H t L = 5 Sin t 2 , 0 < t < 2 where 2 is the signal duration. Here E < 2 * 25 = 50 even if cannot calculate E exactly. 5 Sin t 2 0 < t < 2
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0.5 1.0 1.5 2.0 - 2 2 4 Suppose now we have a communication system in which the Transmitter transmits such a signal H of finite power L to the Reciever . The ensemble of such signals is so large that the Reciever has to be told more before it can figure out what the signal is. One way to do this is to agree that it is of the form for example : a Sin t 2 , 0 < t < 2 where the ' Amplitude' is determined by the Transmitter. The ' Message' is contained in the parameter ' a' which the Reciever does not know and has to figure out. Expanding on this idea , the Transmitted signal is more generally of the form : s H t L = a 1 s 1 H t L + a 2 s 2 H t L , 0 < t < T, where the functions s 1 H . L and s 2 H . L are known H to the Reciever L but the coeffiecients a 1, a 2 must be deciphered by the receiver. Thus we have the problem : how? Here is how : Given s H . L Calculate 0 T s H t L s 1 H t L dt = a 1 0 T s 1 H t L 2 t + a 2 0 T s 2 H t L s 1 H t L t 0 T s H t L s 2 H t L dt = a 1 0 T s 1 H t L s 2 H t L dt + a 2 0 T s 2 H t L 2 t 2 November.nb
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We thus have 2 linear equations for 2 unknowns .We need only to solve them.
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