Introduction_1 - 10/20/10 1 System and Signals System h(t)...

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Unformatted text preview: 10/20/10 1 System and Signals System h(t) Input Signal x(t) Response y(t) [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 jw Y t y jw H jw X jw Y OR t h t x t Y- = = = Signals Deterministic Random [o/p of radio receiver when there e.g. is no broadcasting, the o/p of speaker when no body is talking, etc] t A t x 50 sin ) ( = Now, if the input is random How can we measure the output? We can use, for example, Convolution 10/20/10 2 Energy and Power Signals: Let be the instantaneous voltage and current respectively, then the energy is : ) ( ) ( t i and t v Classification of is a voltage across The energy dissipated by the signal during the interval is given by: ) 1 ( ) ( resistor for t v ) ( t v 1 - 2 , 2 T T - = 2 2 2 ) ( T T T v d t t v E dt t v E resistor for dt t v R dt t i t v E v v - - - = = = 2 2 ) ( 1 ) ( 1 ) ( ) ( 10/20/10 3 And the average power is: - = 2 2 2 ) ( 1 T T T v d t t v T P Now is an energy signal if : is finite, i.e: , where: ) ( t v v E v E 2 2 2 2 ) ( l i m V d t t v E T T T v - = = While is a power signal if: where, ) ( t v v P - = 2 2 2 ) ( 1 l i m T T T v d t t v T E ( Limited can be dropped ) 10/20/10 4 ( 29 signal power is t v finite A T T A dt t T A dt t A T P t A t v Ex T T T T T T v ) ( 2 2 2 cos 1 2 lim cos 1 lim cos ) ( : 2 2 2 2 2 2 2 2 2 = = + = = = - - In general, periodic signal is a power signal Parsevals Theorem: - - - = = = = = energy dw t v dt t v E signal power C dt t v T P v T n n 2 2 2 2 ) ( 2 1 ) ( ) ( 1 10/20/10 5 energy per unit frequency ( jouls/Hz ). It is called energy spectral density ( or energy density ). Thus, to find the energy, we have to integrate over the frequency band of the signal....
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This note was uploaded on 10/19/2010 for the course ELECTRONIC EE - 421 taught by Professor Dr.debai during the Fall '10 term at King Abdulaziz University.

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Introduction_1 - 10/20/10 1 System and Signals System h(t)...

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