EE 341 HW 5S Spring 2017.pdf

# EE 341 HW 5S Spring 2017.pdf - EE 341 Discrete Time Linear...

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EE 341 Discrete Time Linear Signals and Systems Problem Set #5 Solution Problem 1 (a) Solving for homogeneous solution by setting ?[±] − 1 2 ?[± − 1] = 0 And let ? [±] = ?° ² This yields, ² ³ ´ ²µ³ = 0 ⇒ ° = ³ ´ Therefore, ? [±] = ? ( ³ ´ ) ² (b) Soling for particular solution by setting, ?[±] − 1 2 ?[± − 1] = ¶[±] And let ?[±] = · ( ³ 3 ) ² and ¶[±] = ( ³ 3 ) ² ¸[±] This yields, at ± ≥ 0 , · ¹ 1 º » ² 1 2 · ¹ 1 º » ²µ³ = ¹ 1 º » ² ⇒ · − 1 2 · × º = 1 ⇒ · = −2

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