Hw8 P-10.5 - Problem P-10.5 EEL 3135: Signals and Systems...

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Problem P-10.5 EEL 3135: Signals and Systems G. Heitman Electrical and Computer Engineering University of Florida Spring 2006 T0 8 := ω 0 2 π T0 := d 2 T0 := sinc z () i f z 0 = 1 , sin π z π z , := ak ( ) 10 d sinc d k := (b) Plot of spectrum of x(t) k1 0 10 .. := 8 6 4 20 2468 2 2 4 10 d sinc d k ω 0 k ω 0 8 6 4 1 2 3 k ω 0 EEL 3135 1 P-10.5.mcd
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8 6 4 20 2468 2 4 π arg a k () k ω 0 (c) Ideal highpass filter H ω 1 Φω π 8 + π 8 := ω 10 −ω 0 10 0 0.01 + , 10 ω 0 .. := 8 6 4 0.5 1 H ω π 8 ω EEL 3135 2 P-10.5.mcd
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8 6 4 20 2468 1 2 3 H ω () ak ω k ω 0 , Fourier coefficients of the output: bk Hk ω 0 := 8 6 4 1 2 3 k ω 0 8 6 4 2 4 arg b k k ω 0 EEL 3135 3 P-10.5.mcd
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This should be x(t) with the dc removed; i.e. x(t) shifted down by its dc level, 10 d 2.5 = yt () 50 50 m bm ( ) exp i m ⋅ω 0 t = := t1 0 9.99 , 10 .. := 10 50 51 0 5 5 10 2.5 t Why is the plot not a perfect square wave? (d) Ideal lowpass filter ω co 3 2 ω 0 := H ω () Φω ω co + Φω ω co := 8 6 4 20 2468 1 2 3 H ω ak ω k ω 0 , EEL 3135 4 P-10.5.mcd
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Fourier coefficients of the output: b k () Hk ω 0 ak := 8 6 4 20 2468 1 2 3 bk ω 0 k ω 0 This should be a sinusoid of frequency ω 0 with dc level
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Hw8 P-10.5 - Problem P-10.5 EEL 3135: Signals and Systems...

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