# HW2 - EE 3120 Summer 2004 Homework 2 Assigned Friday...

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EE 3120 Summer 2004 Homework 2 Assigned: Friday June,18 Due: Friday June 25 Do not write on this sheet and turn it in. Do all work on other engineering paper. 1. Consider a linear time-invariant lumped system. Let y i be the output excited by the input u i and the initial state x i (0), I = 1,2,3. If x 1 (0) = x 2 (0) = x 3 (0) = a = 0, which of the following statements are correct? a. If u 3 = u 1 + u 2 , then y 3 = y 1 + y 2 . b. If 3 1 2 0.5 ( ) u u u = + , then 3 1 2 0.5 ( ) y y y = + c. If 3 1 2 u u u = - , then 3 1 2 y y y = - 2. What system properties can be deduced from the two permissible input/output pairs? 3. Discuss whether or not each of the following equations is memoryless, linear, time-invariant, and causal: 2 a) ( ) 2 3 ( ) b) ( ) ( ) c) ( ) ( ) ( 1) d) ( ) ( ) e) ( ) ( ) f) ( ) ( / 2) g) ( ) (2 ) h) ( ) ( ) ( ) i) ( ) ( ) ( ) o o t o t t o t y t u t y t u t y t u t u t y t tu t y t u t y t u t y t u t y t u d y t y t u d y t τ = - + = = - = = - = = = + = +

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4. Consider the system shown in the figure below, in which the diodes are assumed
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HW2 - EE 3120 Summer 2004 Homework 2 Assigned Friday...

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