S08.exams1 - ECE 320 Networks and Systems Exam 1 Tuesday...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 320 Networks and Systems Exam 1 Tuesday, February 19, 2008 Closed Book. Closed Notes. No Calculator. 100 Points Total. No credit without explaining your work. 1. (33 pts.=11+11+11) A staircase quantizer Q is defined by two strictly increasing sequences { q j : j = 0 , 1 , . . . , n } and { τ j : j = 0 , 1 , . . . , n, n + 1 } , with τ 0 = -∞ and τ n +1 = + , by ( x IR) Q ( x ) = q j if τ j x < τ j +1 . (1) Suppose n = 3, τ 0 = -∞ , τ 1 = 0, τ 2 = T , τ 3 = 2 T , and τ 4 = + (where T is a constant), and q 0 = 0, q 1 = v , q 2 = 2 v , q 3 = 3 v (where v is a constant). Suppose the input to Q is a random variable denoted by X . Then the output of Q is also a random variable, which is denoted by Y . Define the quadratic error, a random variable denoted by Z , by Z = ( X - Y ) 2 . Suppose X is a continuous random variable with a pdf that is uniform on the interval [ - T, 3 T ] ( T here and T in the definition of τ i are the same T ). (a) Plot the graph of Q . (b) Compute E [ Z ] which depends on T and v . Hint: There are several approaches since you can write E [ Z ] = Z zp Z ( z )d z = Z [ x - Q ( x )] 2 p X ( x )d x.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern