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Unformatted text preview: 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 justresolved distances (according to Rayleighs resolution criterion given in the notes) for a system having a square frequency response H ( X , Y ) = rect 2 parenleftBig X 2 max , Y 2 max parenrightBig and for one having a disk frequency response H ( ) = rect parenleftBig 2 max parenrightBig , where max = 5 mm 1 . Which system would you rather use for imaging and why? Hint: MATLABs fzero function may be useful here. 2. [5] Prove Parsevals theorem for the 2D FT. 3. [5] Prove the rotation property of the 2D FT. 4. [5] Find a version of Parsevals theorem that is appropriate for circularly symmetric functions. 5. [15] Generalize the three main results of Shannons 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 X Y integraldisplay ( m +1 / 2) Y ( m 1 / 2) Y integraldisplay ( n +1 / 2) X ( n 1 / 2) X g a ( x,y ) d x d y ....
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This note was uploaded on 04/19/2011 for the course EECS 556 taught by Professor Staff during the Winter '08 term at University of Michigan.
 Winter '08
 STAFF
 Image processing

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