Lecture_14_Sampling - Sampling EE 341 Discrete Time Linear...

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Sampling EE 341 Discrete Time Linear Systems Fall 2007 Howard Jay Chizeck University of Washington Seattle, Washington Ref: Text 5.4
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31 Oct 2007 2 Linear Time Invariant Systems • Sinusoid in yields a sinusoid out, at the same frequency, but with possibly different gain and phase The gain and phase effect of the system H is a function of frequency This is the same for continuous time and discrete time systems—a fundamental property of linear time invariant systems
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31 Oct 2007 3 To sample x(t), we will multiply it by p(t) A periodic signal !
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31 Oct 2007 4 x=
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31 Oct 2007 5 X(T) X(2T) X(3T) X(0) 0T2 T Signal x s (t) consists of a train of continuous time impulses—take off the arrow heads to get x[n], a discrete time signal
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31 Oct 2007 6 Consider this in the frequency domain—take Fourier Transform of x(t) Not actual shape—drawn this way for pedagogical convenience ω |X ( ω )| x(t) ω b "bandwidth"
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31 Oct 2007 7 Using the continuous-time Fourier Transform of periodic signals since p(t) is periodic (Recall/review Fourier Series for periodic continuous time functions)
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31 Oct 2007 8
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Lecture_14_Sampling - Sampling EE 341 Discrete Time Linear...

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