PS0 10 - University of Minnesota Dept of Electrical and...

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

View Full Document Right Arrow Icon
University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 Problem Set 0 Assigned: January 26, 2010 Due: February 2, 2010 Problem 1 This problem is designed to develop the geometric approach to detection and estimation problems. Given three zero-mean random variables x 1 , x 2 and x 3 with covariance matrix: = Λ 1 1 1 23 13 23 12 13 12 λ λ λ λ λ λ . a. Find a random variable z 2 = x 2 + a 1 x 1 such that z 2 is orthogonal to x 1 . b. Find another variable z 3 = x 3 + b 2 x 2 + b 1 x 1 that is orthogonal to x 1 and x 2 . This process is equivalent of the Gram-Schmidt procedure is linear algebra. c. Any random variable y is said to lie in the subspace of x 1 and x 2 if y = c 2 x 2 + c 1 x 1 . Under what condition is x 3 in the subspace of x 1 and x 2 ? Formulate your answer in terms of the elements of the covariance matrix Λ . (Remember that in our view, a random variable x has zero length if E(x 2 ) = 0.) Problem 2
Image of page 1

Info iconThis 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