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1. DTFT Properties and Examples 2. Duality in fs& ft 3. Magnitude/Phase of Transforms and Frequency Responses
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SAMPLING We live in a continuous-time world most of the signals we encounter are CT signals, e.g. x(). How do we convert them into Dt signals x[n? Sampling, taking snap shots of x(t) every Seconds
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then, assuming we choose wM
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Motivation for the Laplace transform CT Fourier transform enables us to do a lot of things, e. g Analyze frequency response of lTi systems Sampling Modulation Why do we need yet another transform? One view of Laplace Transform is as an extension of the Fourier
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Inverse laplace transforms Laplace Transform Properties The System Function of an Lti System Geometric Evaluation of laplace Transforms and Frequency responses
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Last time: Unit circle (=1) in the ROCDTFT X(@) exists Rational transforms correspond to signals that are linear combinations of DT exponentials
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Geometric Evaluation of z-Transforms and dT Frequency Responses First- and Second-Order Systems System Function Algebra and block diagrams Unilateral z-Transforms
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 2 Issued: October 7. 2003
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Reading Assignments: Lectures #3-4 PS#2: Chapter 2 of O&w Lectures #5-6& PS#3: Chapter 3 of o&w Exercise for home study (not to be turned in, although we will provide solutions)
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 PROBLEM SET 1 SOLUTIONS (E1)(O&W154) (a) For the r=l case, we have
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