Fa 2004 Ch 3 lecture 1A

# Fa 2004 Ch 3 lecture 1A - EE 3120 Chapter 3 Time Domain...

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Unformatted text preview: EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems EE 3120 Linear Systems Analysis Chapter 3 Elementary discrete-time signals and their manipulation f(t) analog signal for t in ( , )- sampling f(t) with sampling period T > 0 gives a discrete time (D-T) signal , where n is an integer ranging from- to Define: is a sequence of numbers assumes T = 1 D-T signals are also called sequences. Positive time sequences Negative time sequences for k < 0 for k > 0 . D-T 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 D-T sequences from C-T signals. Sequences can be manipulated much the same way we manipulated C-T signals. f ( nT ) f [ nT ]:= f ( nT ) f ( nT ) f [ n ]=0 f [ n ]=0 Example: is sampled every T = 0.1 seconds. The D-T sequence would be: ( ) t x t e- = 0.1 ( ) [ ] t n t nT x nT e e x n-- = = = = C/D D-T system D/C x ( t ) x [ n ] ( ) y t y [ n ] C-T signal is sampled to convert to a D-T signal Signal is processed by a D-T system. C-T signal constructed from the output sequence We can use a D-T system to process a C-T signal by sampling the C-T signal and applying the resulting sequence to the D-T systems, then constructing the output C-T 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 discrete-time 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 discrete-time signals and their manipulation EE 3120 Linear Systems Analysis...
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Fa 2004 Ch 3 lecture 1A - EE 3120 Chapter 3 Time Domain...

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