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EE200_Weber_10-7

# EE200_Weber_10-7 - ∗ h 2[n δ[n System 2 h 2[n System 1 h...

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22 EE 200 Cascading LTI Systems Output of the first system becomes the input to the second. Output of the second is the output of the cascade configuration. Commutative and associative properties of convolution means LTI systems can be cascaded in any order. x[n] System 1 h 1 [n] System 2 h 2 [n] x[n] h 1 [n] (x[n] h 1 [n]) h 2 [n] x[n] System 2 h 2 [n] System 1 h 1 [n] x[n] h 2 [n] (x[n] h 2 [n]) h 1 [n]]

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23 EE 200 Cascading LTI Systems Impulse of the overall system is the convolution of the individual impulse responses. Same result if cascaded in different order Equivalent system: δ [n] System 1 h 1 [n] System 2 h 2 [n] h 1 [n] h 1 [n]
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Unformatted text preview: ∗ h 2 [n] δ [n] System 2 h 2 [n] System 1 h 1 [n] h 2 [n] h 2 [n] ∗ h 1 [n]] δ [n] Cascade System h[n]=h 1 [n] ∗ h 2 [n] h 1 [n] ∗ h 2 [n] 24 EE 200 Computing the Convolution Sum 2 1 1 2 3 4 h[n] n 2 1 1 2 3 4 x[n] n h [0] = 1 h [1] = 2 h [2] = 2 h [3] = 1 x [0] = 2 x [1] = " 1 x [2] = 1 n h[n] x[n] x[0]h[n-0] x[1]h[n-1] x[2]h[n-2] y[n] 0 1 2 2 1 0 0 0 2 -1 1 0 0 n<0 0 1 2 3 4 5 n>5 0 2 4 4 2 0 -1 -2 -2 -1 0 1 2 2 1 0 2 3 3 2 1 1 y[n] n 1 2 3 4 5 6 4 3 2 1-1 y [ n ] = x ( k ) h ( n " k ) k = 2 #...
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EE200_Weber_10-7 - ∗ h 2[n δ[n System 2 h 2[n System 1 h...

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