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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.  Find the just-resolved 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.  Prove Parsevals theorem for the 2D FT. 3.  Prove the rotation property of the 2D FT. 4.  Find a version of Parsevals theorem that is appropriate for circularly symmetric functions. 5.  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
- Image processing