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Unformatted text preview: EE 3120 Chapter 3 Time Domain Analysis of DiscreteTime Systems EE 3120 Linear Systems Analysis Chapter 3 Elementary discretetime signals and their manipulation f(t) analog signal for t in ( , ) sampling f(t) with sampling period T > 0 gives a discrete time (DT) signal , where n is an integer ranging from to Define: is a sequence of numbers assumes T = 1 DT signals are also called sequences. Positive time sequences Negative time sequences for k < 0 for k > 0 . DT sequences will be noted by x [ n ], y [ n ]. Where n takes on only integer values and x [ n ] denotes the n th number in the sequence. The square brackets will distinguish DT sequences from CT signals. Sequences can be manipulated much the same way we manipulated CT signals. f ( nT ) f [ nT ]:= f ( nT ) f ( nT ) f [ n ]=0 f [ n ]=0 Example: is sampled every T = 0.1 seconds. The DT sequence would be: ( ) t x t e = 0.1 ( ) [ ] t n t nT x nT e e x n = = = = C/D DT system D/C x ( t ) x [ n ] ( ) y t y [ n ] CT signal is sampled to convert to a DT signal Signal is processed by a DT system. CT signal constructed from the output sequence We can use a DT system to process a CT signal by sampling the CT signal and applying the resulting sequence to the DT systems, then constructing the output CT signal from the output sequence . ( ) y t y [ n ] EE 3120 Linear Systems Analysis [ ] 1 f k = is a two sided sequence, the discrete counterpart of the constant function [ ] 1 k = Impulse sequence Kronecker delta sequence k k = if i is a fixed integer ; [ ] k i [ ] k shifts to k i = [ ] 1 k i = k i = k i k k Chapter 3 Elementary discretetime signals and their manipulation EE 3120 Linear Systems Analysis [ ] [ ] [ ] i f k f i k i = = Impulse Sequence Could be samples of an analog signal [ 2] 4 f = [ 1] f = [0] 2 f = [1] f = [2] 5 f =  [3] 1 f = [ ] 4 [ 2] 2 [ ] 5 [ 2] [ 3] f k k k k k = + + + to k is fixed, i ranges from e.g. k = 10 [10] [ ] [10 ] i f f i i = = every [10 ] i is 0 as ( , ) i 10 i = except at 10 i = [10 ] i [0] 1 = = Chapter 3 Elementary discretetime signals and their manipulation EE 3120 Linear Systems Analysis...
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This note was uploaded on 02/06/2012 for the course EE 2120 taught by Professor Aravena during the Fall '08 term at LSU.
 Fall '08
 ARAVENA

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