hw2 - 16:04 Homework#2 EECS 556 W11 Due Fri Jan 21 by...

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

View Full Document Right Arrow Icon
January 11, 2011 16:04 1 Homework #2, EECS 556, W11. Due Fri. Jan. 21 , by 1:00PM Skills and Concepts 2D FT, sampling, filtering via 2D FFT Problems 1. [15] Find the just-resolved distances (according to Rayleigh’s resolution criterion given in the notes) for a system having a “square” frequency response H ( ν X , ν Y ) = rect 2 parenleftBig ν X 2 ν max , ν Y 2 ν max parenrightBig and for one having a “disk” frequency response H ( ρ ) = rect parenleftBig ρ 2 ν max parenrightBig , where ν max = 5 mm - 1 . Which system would you rather use for imaging and why? Hint: M ATLAB ’s fzero function may be useful here. 2. [5] Prove Parseval’s theorem for the 2D FT. 3. [5] Prove the rotation property of the 2D FT. 4. [5] Find a version of Parseval’s theorem that is appropriate for circularly symmetric functions. 5. [15] Generalize the three main results of Shannon’s ideal “impulse” sampling theory to the more realistic case where we account for finite detector size in the sampling relationship: g d [ n, m ] = 1 Δ X Δ Y integraldisplay ( m +1 / 2)Δ Y ( m - 1 / 2)Δ Y integraldisplay ( n +1 / 2)Δ X ( n - 1 / 2)Δ X g a ( x, y ) d x d y .
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