{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

problem_set7 - EE 511 Problem Set 7 Due on 16 Nov 2007 1...

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

View Full Document Right Arrow Icon
EE 511 Problem Set 7 Due on 16 Nov 2007 1. Let ˆ X t be the Hilbert transform of the W.S.S. random process X t . Show that (i) S ˆ X ( f ) = S X ( f ), (ii) S X ˆ X ( f ) = - S ˆ XX ( f ), (iii) E [ X t ˆ X t ] = 0, and (iv) for Z t = X t + j ˆ X t , determine S Z ( f ) in terms of S X ( f ). 2. The power spectrum of a W.S.S. band-pass random process X t is as shown in Figure 1. Sketch S X I ( f ), S X Q ( f ) and S X I X Q ( f ) assuming 5 MHz to be the carrier frequency. S (f) X f(MHz) 4 5 7 -7 -5 -4 1 Figure 1: 3. Repeat problem 2 assuming 4 MHz to be the carrier frequency. 4. A narrow-band noise process N t has zero-mean and auto-correlation function R N ( τ ). Its power spectral density S N ( f ) is centered about ± f c . The in-phase and quadrature compo- nents N I t and N Q t are defined by N I t = N t cos 2 πf c t + ˆ N t sin 2 πf c t and N Q t = ˆ N t cos 2 πf c t - N t sin 2 πf c t . Show that R N I ( τ ) = R N Q ( τ ) = R N ( τ ) cos 2 πf c τ + ˆ R N ( τ ) sin 2 πf c τ and R N I N Q ( τ ) = - R N Q N I ( τ ) = R N ( τ ) sin 2 πf c τ - ˆ R N ( τ ) cos 2 πf c τ , where ˆ R N ( τ
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