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Unformatted text preview: Week 04: Part 1 Review: Sampling and Aliasing 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 continuoustime (CT) of a function ( x(t) ) every T second. T is the sampling period X[n] 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? Page 3 ECTE906 Advanced Signals & Systems Spring 2009 Review: DT versus CT Digital computers represent and manipulate continuoustime (CT) signals numerically (MATLAB) or symbolically (Mathematica, Maple) Any computer representation is discrete A DT signal is represented mathematically by an indexed sequence of numbers. The signal values would be indexed by memory address while they are in memory locations in a computer DT signals are obtain through 1 Sampling CT signal at equally spaced time intervals 2 Computing the values of DT signal directly from a formula DiscreteTime Signal; the word sequence could be used in place of signal, or the adjective digital in place of discretetime NOTE: Analogue waveforms (waves, functions) is plotted by MATLAB by connecting isolated (discrete) points in time rather than plotting a continuoustime waveform Page 4 ECTE906 Advanced Signals & Systems Spring 2009 Introduction: A/D Conversion & Reconstruction In many common situation in engineering a function f(t) is sampled. When a signal is evaluated by numerical procedure, it is always necessary to sample the function since digital computers cannot deal with continuous (analogue) functions. If the signal to be analysed is analogue in nature it must be converted into digital form by an analogue to digital (A/D) converter. One of the most widely used application of A/D converter is where computers and microcontrollers are employed to automate processes (decision making) and react to input data for generation of desired output signal (s). The problem is how to choose the sampling interval T s so that the original analog signal can be reconstructed Page 5 ECTE906 Advanced Signals & Systems Spring 2009 A typical application of D/A conversion (Modulation) swf animation (source: ForuzanData Communication and Networking) Page 6 ECTE906 Advanced Signals & Systems Spring 2009 Systems & Signals Systems process signals Processing Goals: Change x(t) into y(t) For example, more BASS Response (Home Theatre, audio...
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