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SP 2005 CH 3 DT Convolution

# SP 2005 CH 3 DT Convolution - EE 3120 Chapter 3 Time Domain...

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EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems Discrete-Time Convolution

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Discrete Convolution Gives the zero state response Also called the input-output description Applicable to ANY LTI system that is also causal and initially relaxed at n = 0 (no initial conditions) Also can be written 0 [ ] [ ] [ ] [ ] [ ] i y n x i h n i x n h n = = - =
[0] [0] [0] [1] [0] [1] [1] [0] [2] [0] [2] [1] [1] [2] [0] y x h y x h x h y x h x h x h = = + = + + . . . Executing a D-T Convolution Three common ways of calculating a DT convolution by hand: Each method requires knowledge of the input and the impulse response. Mathematical Tabular Graphical Mathematical: 0 [ ] [ ] [ ] n i y n x i h n i = = -

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Tabular method: [ ] {1,2,3,4, 1,...} [ ] { 1,1, 3,2...} h n x n = - = - - [ ] h n [ ] x n -1 1 -3 2 . . . 1 2 3 4 -1… -1 -2 -3 -4 1 1 2 3 4 -1 -3 -6 -9 -12 3 2 4 6 8 -2 [0] y [1] y [2] y [3]... y [0] 1 y = - [1] 1 2 1 y = - = - [2] 3 2 3 4 y = - + - = - [3] 2 6 3 4 5 . . . y = - + - = - [ ] { 1, 1, 4, 5,...} y n = - - - - Fill in table using multiplication: Execute addition on angles: We can only calculate the first 4 values of this convolution accurately, why?
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SP 2005 CH 3 DT Convolution - EE 3120 Chapter 3 Time Domain...

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