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Unformatted text preview: CAULEY OCT 1, 2009 ECE 301 Midterm Examination #1 Solutions 1. Enter your name, student ID number, e-mail address, and signature in the space provided on this page, NOW! 2. You have one hour . 3. There are 10 pages in the exam booklet. Use the back of each page for rough work, if necessary. 4. You are not allowed the use of crib sheets. 5. You are not allowed the use of calculators. 6. Tip: Make sure you read through the exam once before beginning. Work as quickly and efficiently as you can. If you get stuck on a certain problem, move on to others. Name: Student ID #: E-mail address: Signature: 1 1. (20 points) This problem has two parts: Part I Enter your answers in Table I on page 3. For each entry in the table, write “ Y ” if you can conclude that the property listed on the left holds for the system listed at the top of the column. Enter “ N ” if it can be concluded that the property does not hold. (For each case, there is sufficient data to make this decision.) Every entry in the table is worth 1 point. (a) System I : y [ n ] = x [ n ] sin ( π 3 n ) . Solution: i. Only depends on input at current time → Memoryless → Causal. ii. If the input x 1 [ n ] = δ [ n- 6 ] , we have: y 1 [ n ] = δ [ n- 6 ] sin ( π 3 n ) = δ [ n- 6 ] sin ( π 3 6 ) = δ [ n- 6 ] sin ( 2 π ) = 0. This is the same output as if we had x 2 [ n ] = → not invertible....
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