Chap6StudentSolutions

10e 6 rect f 10 f 10e 6 j rect f

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Unformatted text preview: f (t ) and x 2 f (t ) . 6 y( t) = sinc( t) sin(20πt) + rect ( t) cos(20πt) π X1d ( f ) = F sinc ( t ) sin ( 20π t ) + rect ( t ) cos ( 20π t ) sin 20π t − 6 Solutions 6-29 M. J. Roberts - 8/16/04 j rect ( f ) ∗ [δ ( f + 10) − δ ( f − 10)] πf −j j 2 X1d ( f ) = ∗ [δ ( f + 10) − δ ( f − 10)]e 60 + sinc( f ) ∗ 1 [δ ( f − 10) + δ ( f + 10)] 2 2 πf −j j j[rect ( f + 10) − rect ( f − 10)] ∗ [δ ( f + 10) − δ ( f − 10)]e 60 X1d ( f ) = 4 +[sinc( f − 10) + sinc( f + 10)] πf πf −j −j 60 − δ ( f − 10)e 60 rect ( f + 10) ∗ δ ( f + 10)e j πf πf − rect ( f − 10) ∗ δ ( f + 10)e − j 60 − δ ( f − 10)e − j 60 j X1d ( f ) = πf πf 4 −j −j sinc( f − 10) ∗ δ ( f + 10)e 60 − δ ( f − 10)e 60 + πf πf −j −j + sinc( f + 10) ∗ δ ( f + 10)e 60 − δ ( f − 10)e 60 π π −j j rect ( f + 10) ∗ δ ( f + 10)e 6 − rect ( f + 10) ∗ δ ( f − 10)e 6 j π π − rect ( f − 10) ∗ δ ( f + 10)e j 6 − rect ( f − 10) ∗ δ ( f − 10)e − j 6 j X1d ( f ) = π π 4 j − j sinc( f − 10) ∗ δ ( f + 10)e 6 − sinc( f − 10) ∗ δ ( f − 10)e 6 + π π j −j + sinc( f + 10) ∗ δ ( f + 10)e 6 − sinc( f + 10) ∗ δ ( f − 10)e 6 π π π π j −j j −j j rect ( f + 20)e 6 − rect ( f )e 6 − rect ( f )e 6 + rect ( f − 20)e 6 j X1d ( f ) = π π π π 4 j −j j −j + sinc( f )e 6 − sinc( f − 20)e 6 + sinc( f + 20)e 6 − sinc( f )e 6 π π j −j π j rect ( f + 20)e 6 − 2 cos rect ( f ) + rect ( f − 20)e 6 6 j X1d ( f ) = π π 4 −j j + j 2 sin π sinc( f ) − sinc( f − 20)e 6 + sinc( f + 20)e 6 6 Solutions 6-30 M. J. Roberts - 8/16/04 Now apply the lowpass filter, X1 f ( f ) = j π π − j 2 cos 6 rect ( f ) + j 2 sin 6 sinc( f ) 4 X1 f ( f ) = x1 f ( t) = 1 π π cos 6 rect ( f ) − sin 6 sinc( f ) 2 1 π π cos 6 sinc( t) − sin 6 rect ( t) 2 Similarly, x 2 f ( t) = 1 π π cos 6 rect ( t) + sin 6 sinc( t) 2 Quadrature Demodulated and Filtered Signal x1f(t) 1 -4 4 -0.25 t In-phase Demodulated and Filtered Signal x2f(t) 1 -4 4 -0.25 t 38. A...
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This note was uploaded on 06/19/2013 for the course ENSC 380 taught by Professor Atousa during the Spring '09 term at Simon Fraser.

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