This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full Document
 Fall '08
 ARAVENA
 Signal Processing, Linear Systems Analysis, Elementary DiscreteTime Signals

Click to edit the document details