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) x n ( ) 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. b t ( ) t 0 = b n ( ) b t ( ) t nT s = = DT signal CT signal, evaluated at integer multiples of the sampling period T s We write x n [ ] Hemami 220 Lec DT - 4 Beethoven’s Fifth Example b t ( ) t b t ( ) t b n ( ) n Continuous time signal Samples superimposed on CT signal Discrete time signal T s 2T s 3T s 4T s 6T s 1 2 3 4 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.
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