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20105ee211A_1_ComputerAssignment2 - EE 211A Fall Quarter...

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1 EE 211A Digital Image Processing I Fall Quarter, 2010 Handout 9 Instructor: John Villasenor Computer Assignment 2 IIR filtering, transforms of 2D functions and images Due: Thursday, 21 October 2010 What to turn in: 1. Code for implementing the IIR filter of section I. Please only turn in the lines of code where the actual filtering is performed. Please comment this section of code well, indicating how you are handling the possibility of negative index values. 2. Comments (several sentences) on the effect of the IIR filter on the image panic.gray (Section I, Part 2). 3. Statement of stability for the IIR filter for the three cases of a, b in Section I, Part 3. 4. Comments (several sentences) on the Fourier and discrete cosine transforms obtained in Section II, Parts 6 and 7. 5. Compare, in a sentence or two, the results of reconstructing a signal from Fourier magnitude only or Fourier phase only. 6. A statement of the number of non-zero pixels in the autocorrelation described in Section II, Part 9. I IIR Filtering Consider the 2D IIR filter ) , ( ) 1 , 1 ( ) , 1 ( ) , ( n m x n m by n m ay n m y - - - = In class we determined that the impulse response ) , ( n m h of this filter has first quadrant wedge support. Using intro.c as a template, write a program which calculates ) , ( n m y for 0 , m 1 - N n . Be sure to enforce zero boundary conditions by initializing , 0 ) , ( = n m y and by including provisions in your program for cases where the array index values 1 - m or 1 - n are less than 0. In addition, be sure that you choose a valid path for the recursive computation of ) , ( n m y . When your program is ready, run it for the following cases:
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2 1. Let ), , ( ) , ( n m n m x δ = so that ) , ( n m y will be the impulse response. For the filter coefficients use . 58 . 0 = = b a (this is an unstable filter but it will serve to illustrate , h R the region of support of the impulse response). Calculate ), , ( n m y
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