{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm1_w09 - (b(20 How would you reconstruct x t from x n...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE352: Signals & Systems II Dr. Raviv Raich Midterm I (Feb 11, 2009) The duration of the exam is fifty minutes (3:00pm-3:50pm). Only one sheet of formulae is allowed. No calculators are allowed. Return this copy of the exam form along with formulae sheet and your notes. 1. ( 100%+10% bonus) In the following, we will consider the problem of reconstruction from an incomplete set of samples. We are given a sampling system in which each third sample is set to zero due to a circuit malfunction. We use the following diagram to represent the system: × × x ( t ) X ( ) W - W x δ ( t ) p ( t ) q [ n ] x [ n ] y [ n ] C/D Where p ( t ) = n = -∞ δ ( t - nT s ) and q [ n ] = k = -∞ δ [ n - 3 k ] + δ [ n - 3 k - 1] . (a) (20%) Express X δ ( ) (the Fourier Transform (FT) of x δ ( t ) ) in terms of X ( ) (the FT of x ( t ) ). Sketch X δ ( ω
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . (b) (20%) How would you reconstruct x ( t ) from x [ n ] ? Explain the process in both the frequency domain and time domain (use diagrams and equations to make your explanation precise). (c) (20%) Find Q ( e j Ω ) the DTFT of q [ n ] and sketch it. (d) (20%) Express Y ( e j Ω ) in terms of X ( e j Ω ) . Express Y ( e j Ω ) in terms of X ( jω ) . Sketch Y ( e j Ω ) . (e) (20%) For W = π 3 T s , how would you reconstruct x ( t ) from y [ n ] ? Explain the process in both the frequency domain and time domain (use diagrams and equations to make your precise). (f) Bonus (10%) For W = 2 π 3 T s , how would you reconstruct x ( t ) from y [ n ] ?...
View Full 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