090109Lecture03

090109Lecture03 - Lecture 3 Wi 09 ECE 700 Digital Signal...

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1 Lecture 3 Wi 09 ECE 700 Digital Signal Processing Lecture 3 01/09/09
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2 Lecture 3 Wi 09 Interpolation [] x n Discrete-time Processing x ( t ) Ideal sampling Ideal sampling Period = T s yn Period = T/L s Revisit: Interpolation is the method used to increase the sampling rate by an integer factor.
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3 Lecture 3 Wi 09 Interpolation = Upsampling + Filtering 0 π 2 π -2 ππ 0 π 2 π -2 0 π 2 π -2 L x [ n ] y 1 [ n ] Ideal LPF ω c = π / L DC Gain = L v [ n ] L =2
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4 Lecture 3 Wi 09 Why does this work? 12 () ( ) 2 ( ) / 1 2 / ( ) ( ) ( ) / j c k j c k jj L cc kk k Xe X j TT Lk Ye L k L V e X e Xj T T L ω ωω ωπ π =−∞ ∞∞ = = −− == = ∑∑ After ideal lowpass filtering with a cutoff freq. of π / L and a gain of L , 1 2/ 2 ( ) ( ) // j k l L L L l L T T L πω Z
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5 Lecture 3 Wi 09 Interpolation in the time domain 1 / integer [] , i n t e g e r 0, otherwise [][ ] [ ] ] k k kL r nn x vn LL yn vkhn k k xh n k L xrhn rL =−∞ = =− = L x [ n ] y 1 [ n ] Ideal LPF ω c = π / L DC Gain = L v [ n ]
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6 Lecture 3 Wi 09 Practical reconstruction using ZOH
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090109Lecture03 - Lecture 3 Wi 09 ECE 700 Digital Signal...

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