Fa 2004 Ch 3 lecture 1A

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

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EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems
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EE 3120 Linear Systems Analysis Chapter 3 Elementary discrete-time signals and their manipulation (, ) −∞∞ sampling f(t) with sampling period T > 0 f(t) analog signal for t in f ( nT ) , where n is an integer ranging from gives a discrete time (D-T) signal −∞ to Define: assumes T = 1 . f [ nT ]:= f ( nT ) f ( nT ) is a sequence of numbers D-T signals are also called sequences. 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. for k < 0 f [ n ]=0 Positive time sequences Negative time sequences f [ n ]=0 for k > 0
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Example: is sampled every T = 0.1 seconds. The D-T sequence would be: () t xt e = 0.1 [ ] tn T x nT e e x n −− = == = 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 . yt y [ n ] x ( t ) x [ n ] y [ n ] C/D D-T system D/C 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
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EE 3120 Linear Systems Analysis [] 1 fk = is a two sided sequence, the discrete counterpart of the constant function 0 [] 1 k ∂= Impulse sequence Æ Kronecker delta sequence 0 0 k k = Chapter 3 Elementary discrete-time signals and their manipulation k k ki = if i is a fixed integer ; k ∂− shifts to = 0 1 ∂−=
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EE 3120 Linear Systems Analysis Impulse Sequence Æ Could be samples of an analog signal Chapter 3 Elementary discrete-time signals and their manipulation [2 ] 4 f −= [1 ] 0 f [0] 2 f = [1] 0 f = [2] 5 f = − [3] 1 f = [] 4[ 2 ] 2[] 5[ 2 ] [ 3 ] fk k k k k =∂ + +∂ −∂ − + ∂ − [] [][ ] i fi k i =−∞ =∂ −∞ to k is fixed, i ranges from e.g. k = 10 [10] [ ] [10 ] i ff ii = ∂− 10 i = [10 ] i (, ) i →−∞∞ every is 0 as except 10 i = ] i [0] 1 = at Æ =
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EE 3120 Linear Systems Analysis Chapter 3
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Fa 2004 Ch 3 lecture 1A - EE 3120 Chapter 3 Time Domain...

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