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w04-p2-spectrum-view-sampling-2up

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Week 04: Part 2 – Review: Spectrum View of Sampling and Reconstruction Main Text: Signal Processing First, J. H. McClellan, R.W. Schafer & M.A. Yoder ECTE906 – Advanced Signals & Systems Master of Engineering Studies Main Source: The subject textbook as well as the following URL; http://users.ece.gatech.edu/mcclella/SPFirst/LectureSlides/SPFirstLectureSlides.html This document also makes use of an earlier document prepared by D. Sutanto Parviz Doulai SECTE/Spring Session – 2009 Page 2 ECTE906 – Advanced Signals & Systems- Spring 2009 Introduction: Taking Snap Shots Sampling means taking snap shots of a continuous-time (CT) of a function ( x(t) ) every T second. T is the sampling period X[n] Ξ x(nT), n= . . . -1, 0, 1, 2, . . . Many signals could have the same samples! All values of x(t) between sampling points are lost Reconstruction of x(t) from samples; how? Any special conditions?

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Page 3 ECTE906 – Advanced Signals & Systems- Spring 2009 Spectrum View of a Sampling and Reconstruction System The output of the C-to-D converter is a discrete-time signal with an infinite number of aliases. The spectrum diagram of a sampling operation includes all of aliases associated with the generated DT signal. The folding and aliasing of frequencies associated with sampling and reconstruction system can be tacked via the movement of spectrum lines in the frequency domain. Frequency spectrum explanation of the sampling process gives an easy view of this process and its limitations. COMPUTER Ideal D-to-C Ideal C-to-D x(t) y(t) y[n] x[n] Sampling and reconstruction system Page 4 ECTE906 – Advanced Signals & Systems- Spring 2009 Systems View of Sampling and Reconstruction The systems view of sampling and reconstruction looks at: Ideal Reconstruction System Ideal System Including Anti-Aliasing Reconstruction with Hold Operation http://cnx.org/content/m11465/latest/
Page 5 ECTE906 – Advanced Signals & Systems- Spring 2009 Spectrum Plot of Discrete-Time Signal Spectrum plot is considered very useful for representation of CT sinusoidal signals.

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