EECS
finalSolutions

finalSolutions - UNIVERSITY OF CALIFORNIA College of...

• Notes
• 9

This preview shows pages 1–3. Sign up to view the full content.

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences Professor Tse Spring 2005 EECS 20n — Final Exam Solutions [5 pts.] Problem 1 This is a linear constant coefficient system that is initially at rest . [15 pts.] Question 2 (a) (10 pts.) Overall period = 6 (b) (5 pts.) Overall period where are integers. No such exists because 2 is rational and is irrational, . y n ( ) 1 4 -- y n 1 ( ) x n ( ) 1 2 -- x n 1 ( ) + + = LTI q n ( ) 1 2 -- e i 2 π 3 ------ n 1 2 -- e i 2 π 3 ------ n e i π n + + = period 3 period 2 ω 0 2 π 6 ------ = X 2 X 2 1 2 -- = = X 3 1 = X k 0 otherwise = for 2 k 3 v t ( ) π t ( ) t ( ) cos + cos = period 2 period 2 π p 2 m 2 π n = = m n , m n , 2 π not periodic

This preview has intentionally blurred sections. Sign up to view the full version.

2 of 9 [10 pts.] Question 3 (a) (5 pts.) Yes, the system F can be linear. (b) (5 pts.) The system F cannot be time-invariant, because new frequencies have been created that did not exist in . [15 pts.] Question 4 (a) (7 pts.) Reading the signals off the diagram, we have: Written alternatively, the LCCDE describing the system above is: (b) (8 pts.) We note that if is the output of a delay block, then the input to the delay block must be , as shown below: Accordingly, we can label the original delay-adder-gain block diagram with and . We can now read off the diagram the expressions for , , and . Hence, the state-space equations are: ω 0 t ( ) cos y t ( ) x t ( ) X ω ( ) y n ( ) 5 y n 1 ( ) y n 1 ( ) x n 1 ( ) x n ( ) + + = y n ( ) 5 y n 1 ( ) y n 1 ( ) + + x n ( ) x n 1 ( ) + = s i n ( ) s i n 1 + ( ) s i n 1 + ( ) i 1 2 , = D s i n ( ) s 1 n 1 + ( ) s 2 n 1 + ( ) s 1 n 1 + ( ) s 2 n 1 + ( ) y n ( ) s 1 n 1 + ( ) s 2 n ( ) 5 y n ( ) x n ( )} s 1 n 1 + ( ) + 5 s 1 n ( ) s 2 n ( ) 4 x n ( ) + = = y n ( ) s 1 n ( ) x n ( ) + = s 2 n 1 + ( ) y n ( ) = s 2 n 1 + ( ) s 1 n ( ) x n ( ) = s 1 n 1 + ( ) s 2 n 1 + ( ) 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern