Lee2-VS - Signal-Space Analysis ENSC 428 Spring 2008...

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Signal-Space Analysis ENSC 428 – Spring 2008 Reference: Lecture 10 of Gallager
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Digital Communication System
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Representation of Bandpass Signal Bandpass real signal x ( t ) can be written as: ( ) ( ) ( ) cos 2 c xt st ft π = () ( )( ) 2 2 Re where is complex envelop c jf t xte  =  ±± Note that ( ) ( ) ( ) IQ x tx t j =+ ± In-phase Quadrature-phase
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Representation of Bandpass Signal () ( ) ( )() ( ) 2 2Re cos 2 sin 2 2cos 2 2sin 2 c jf t IQ c c Ic Q c xt xte x tj x t f f t x t ft π ππ  =  =+ + ± ±± (1) (2) Note that ( ) ( ) ( ) j t xt e θ = 22 2 cos 2 cc jt t t c e t πθ == ±
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Relation between and 2 2 ( ) xt ( ) ± f x 2 c jf t e π f c -f c f f c f f () ( ) ± () () ( ) * 1 2 , 0 , 0, 0 cc c Xf f X f f Xf f X f Xff f ++  =− + +  > == + < ±± ± 2
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Energy of s ( t ) () 2 2 2 0 2 0 (Rayleigh's energy theorem) 2 (Conjugate symmetry of real ( ) ) Es t d t Sf d f d f s t d f −∞ −∞ = = = = ±
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Representation of bandpass LTI System () ht ( ) ± st ( ) ± ( ) rt ( ) ± () () () ( ) because ( ) is band-limited. c rt st ht Rf SfH f SfHf f s t =∗ = =+ ± ±± ± ± ( ) ( ) ( ) ( ) () ( ) * , 0 0, 0 cc c Hf Hf f H f f Hf f f Hf H f f + + =− + + > = < ±
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Key Ideas
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Examples (1): BPSK
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Examples (2): QPSK
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