Exam1Solutions - ECEN 661 Exam 1 Solutions Spring 2008...

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

View Full Document Right Arrow Icon
ECEN 661 Exam 1 Solutions Spring 2008 Problem 1. (25 points) Zero-mean, white Gaussian noise with a PSD of is passed through a BPF whose transfer function is as described in the figure. (a) Find the variance of the I and Q components of the output bandpass noise. (b) Are the I and Q components of the noise independent? Carefully justify your answer. Solution: Let be the output noise process and its low-pass equivalent. Then . , . . (a) The variance of the I and Q parts is . (b) Since the cross PSD of the I and Q part is zero, its cross-correlation is also zero. Both and are zero-mean Gaussian random process and hence they are uncorrelated and indepen- dent. Half cycle of a sine wave f f c B H f ( ) A N 0 2 n o t ( ) z t ( ) x t ( ) jy t ( ) + = f B 2 --- A 2 N o Φ xx f ( ) Φ n o n o f ( ) N o 2 ----- H f ( ) 2 = Φ xx f ( ) Φ yy f ( ) L.P. Φ n o n o f f c ( ) Φ n o n o f f c + ( ) + { } = = A 2 N o cos 2 π f B ---- = f B 2 < Φ yx f ( ) j L.P. Φ n o n o f f c ( ) Φ n o n o f f c + ( ) { } 0 = = σ 2 Φ xx f ( ) f d 2 A 2 N o cos 2 π f B ---- 0 B 2 df A 2 N o 1 2 π f B -------- cos + f d 0 B 2 A 2 N o B 2 ---------------- = = = = x t ( ) y t ( )
Image of page 1

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

View Full Document Right Arrow Icon
Problem 2. (25 points) The four waveforms listed below are used to form a 4-ary signalling format.
Image of page 2
Image of page 3
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