skemaTest2SEE2043sesi20102011sem1 (1).pdf - NAME IC NO SECTION LECTURER\u2019S NAME SOLUTION SEE2043 SIGNAL AND NETWORKS Test 2(5th OCTOBER 2010 SEM 01

skemaTest2SEE2043sesi20102011sem1 (1).pdf - NAME IC NO...

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1 | s k y 2 0 1 0 NAME SOLUTION IC NO. SECTION LECTURER’S NAME SEE2043 SIGNAL AND NETWORKS Test 2 (5 th OCTOBER 2010) SEM 01 SESSION 2010/2011 Total Pages: 5 QUESTION 1 . a) Let f ( t ) be a signal. It’s Fourier transform is plotted in Figure 1. Sketch the graph of the Fourier transform of the signal e j 4 t f(t). What happened to the spectrum F( ω ) from this operation ? (5 marks) Figure 1 Solution: A phase change in time corresponds to a shift in frequency , F [e j 4 t f(t)] = F ( ω 4), in this case a shift to the right by 4. F ( ω ) 1 2 3 3 7 6 5 4 F ( ω ) 1 2 3 3 2 1 n ω 3 2
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2 | s k y 2 0 1 0 b) Obtain the Fourier transform of the signal y(t) based on the Figure below. (5 marks) Solution: X ( ω ) = 2 2 2 ω α α + A H ( ω ) = 2 sinc ω A Convolution property is applied. Therefore, Y ( ω ) = X ( ω ). H ( ω ) = 2 2 2 ω α α + A 2 sinc ω A h ( t ) = rect( t ) x ( t ) = e - α | t | y ( t ) 1 1 2 1
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