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Ch 1 lecture 3

# Ch 1 lecture 3 - EE 3120 Linear Systems Analysis Lecture 3...

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EE 3120 Linear Systems Analysis Lecture 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 ( ) f kT , where k is an integer ranging from - to [ ]: ( ) f k f kT = Define: ( ) f kT is a sequence of numbers assumes T = 1 D-T signals are also called sequences. Positive time sequences Negative time sequences [ ] 0 f k = [ ] 0 f k = for k < 0 for k > 0 .

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EE 3120 Linear Systems Analysis Lecture 3 Elementary discrete-time signals and their manipulation [ ] 1 f k = is a two sided sequence, the discrete counterpart of the constant function 0 [ ] 1 k = Impulse sequence Kronecker delta sequence 0 0 k k = if i is a fixed integer ; [ ] k i - [ ] k shifts to k i = 0 [ ] 1 k i - = k i = k i k k
EE 3120 Linear Systems Analysis Lecture 3 Elementary discrete-time signals and their manipulation [ ] [ ] [ ] i f k f i k i =- = - Impulse Sequence Could be samples of an analog signal [ 2] 4 f - = [ 1] 0 f - = [0] 2 f = [1] 0 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 = =

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Ch 1 lecture 3 - EE 3120 Linear Systems Analysis Lecture 3...

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