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Unformatted text preview: January 26, 2011 09:36 1 Homework #4, EECS 556, W11. Due Fri. Feb. 4 , by 1:00PM Notes • The grader may not return this HW before Exam 1, so you may wish to keep a copy of your answers. Skills and Concepts • discretespace signals and systems • filter design • DFS, DFT Problems 1. [10] Describe in a couple sentences two possible image processing projects that might interest you. 2. [10] This problem is an elementary preview of the principles underlying transform coding with truncation. A typical digital image x [ n,m ] has a spectrum that decays with increasing spatial frequency. As a concrete model, suppose that  X ( ω X ,ω Y )  = braceleftBigg A e α √ ω 2 X + ω 2 Y , ω 2 X + ω 2 Y ≤ π 2 , otherwise . Suppose that we truncate the tails of this spectrum by as follows: Y ( ω X ,ω Y ) = braceleftbigg X ( ω X ,ω Y ) , radicalbig ω 2 X + ω 2 Y ≤ π/ 10 , otherwise , and then reconstruct the signal y [ n,m ] by an inverse 2D DSFT. (a) [10] For α = 5 , evaluate the normalized root meansquared (RMS) error radicalbigg P ∞ n =∞ P ∞ m =∞  y [ n,m ] x [ n,m ]  2 P ∞ n =∞ P ∞ m =∞  x [ n,m ]  2 ....
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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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