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EE 424 #1: Sampling and Reconstruction

EE424#1: Sampling and ReconstructionJanuary13,2011 ContentsNotation and Definitions2A Review: Signal Manipulations, CT Convolution, CTFT and Its Properties3 Signal manipulations3CT convolution3 CTFT and its properties5 Poisson Sum Formula7 Sampling7 Introduction7 Applications8 Point and impulse sampling8 Sampling theorem11 Reconstruction12 Ideal Reconstruction : Shannon interpolation formula12 Ideal Reconstruction : Summary13A general Reconstruction filter14 Reconstruction with zero-order hold15 Examples of Sampling and reconstruction19 Comments on Lab124 Sampling part of Lab124 Reconstruction part of Lab125 Lowpass Reconstruction filters26DT lowpass Reconstruction filters29 Reading: EE224handouts2,16,18,19, andlctftsummary(review); , , , and the V.

ee 424 #1: sampling and reconstruction 5 CTFT and its properties XF(w) denotes continuous-time Fourier transform (CTFT) of x(t): XF(w) = Z+¥ ¥ x(t) e j w t dt (4a) x(t) = 1 2p Z+¥ ¥ XF(w) ej w t dw (4b) where w is the frequency in radians per second (rad/s). The textbook uses X(j w) to denote the CTFT of x(t). Review EE 224 handout ...

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