SPFirst-L04-SK.pdf - Chapter 4 Sampling and Aliasing Sungoh...

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Chapter 4 Sampling and Aliasing Sungoh Kwon
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Overview Why do we need sampling? 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 2 Continuous Time Signal x(t) Discrete Time Signal x[n] Sampling Reconstruction
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Example 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 T[Sec] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 T[Sec]
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Example 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 4
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Sampling Discrete time signal: an indexed sequence of numbers x[n] Sampling process Convert x(t) to numbers x[n] “n” is an integer; x[n] is a sequence of values Think of “n” as the storage address in memory Uniform sampling at t = nT s Ideal: x[n] = x(nT s ) 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 5
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Sampling Sinusoidal Signals Let x(t)=A cos( ω t+ φ ) Sample x(t) at every T s where is “ normalized radian frequency ” defined as and varies from 0 to 2 p , as f varies from 0 to the sampling f requency 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 6 ) ˆ cos( ) cos( ) ( ] [ n A nT A nT x n x o s s , ˆ s s o f T o ˆ
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Example: Sampling Sinusoidal Signals 9/24/2015 2010 DSP by S.Kwon, University of Ulsan 7 f s 2kHz s s T f 1 500Hz Hz 100 f T s 5 2 500 100 2 2 ˆ p p p s s o f f f
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Aliasing
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  • Spring '18
  • Ulsan, University of Ulsan

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