lectureDT.220.06 - Discrete-time Signals Systems...

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Hemami 220 Lec DT - 1 Discrete-time Signals & Systems Outline DT signals: examples & plotting Definitions Special sequences DT systems you already know ECE 220 Fall 2006 Prof. Hemami Hemami 220 Lec DT - 2 Discrete-time signals Definition — a DT signal is an indexed sequence of numbers. Common variables for the index are the “integer” letters — k, l, m, n Examples Maximum temperature in Ithaca every day in 2004 (366 samples long). , (infinite duration) xn () n 2 5 n 4 + = n << Hemami 220 Lec DT - 3 More DT Signal Examples A DT signal could come from samples. Let represent Beethoven’s Fifth Symphony, with at the beginning. (in an abuse of notation). NOTE — textbook uses square brackets for DT signals. I will not do this; use context/common sense to figure out if it’s a CT or DT signal. bt t 0 = bn tn T s = = DT signal CT signal, evaluated at integer multiples of the sampling period T s We write [] Hemami 220 Lec DT - 4 Beethoven’s Fifth Example t t n Continuous time signal Samples superimposed on CT signal Discrete time signal T s 2T s 3T s 4T s 6T s 12 34 6
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Hemami 220 Lec DT - 5 Plotting DT Signals To plot , or not to plot ? (in Matlab) plot “connects-the-dots” — but DT signals only exist on the integers! For a DT signal, exists, but makes no sense; there is no meaning to the signal when the argument is not an integer. stem is the correct Matlab command to use, and you should always sketch DT signals using the stem “lollypops.” BUT for long signals, stem can make a mess. So
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lectureDT.220.06 - Discrete-time Signals Systems...

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