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MidtermSoln SnS (mine)

MidtermSoln SnS (mine) - Purdue University School of...

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Purdue University School of Electrical and Computer Engineering ECE 301: Signals and Systems SOLUTION Summer 2009 - Midterm Monday, July 13, 2009 No calculators/computers/handhelds of any sort are allowed. No books/notes are allowed except one A-4 size sheet (both sides) is allowed. Note: after the exam, you may want to save this sheet. Please show all of your work. Answers without justification are subject to receiving no credit. If you need extra space, you may use the back of the previous exam page. The exam is 60 minutes long. Good luck! Score: 1. (15 pts.) 2. (30 pts.) 3. (20 pts.) 4. (35 pts.) Total: (100 pts.) 1
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Problem 1. ( 15 points ) Consider a CT system which relates the output y [ n ] to the input x [ n ] as follows: y [ n ] = 3 + nx [ n ] . (a) Indicate with yes or no if this system is: i) memoryless. Yes. The output y [ n ] depends only on x [ n ] for all times n . ii) causal Yes. It is causal because it is memoryless. iii) linear No. Two inputs x 1 [ n ] and x 2 [ n ] produce outputs y 1 [ n ] = 3 + nx 1 [ n ] and y 2 [ n ] = 3 + nx 2 [ n ], respectively. Define a third input x 3 [ n ] = ax 1 [ n ] + bx 2 [ n ] which produces a response y 3 [ n ] = 3 + nx 3 [ n ] = 3 + n ( ax 1 [ n ] + bx 2 [ n ]) negationslash = ay 1 [ n ] + by 2 [ n ] = 3( a + b ) + anx 1 [ n ] + bnx
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