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20105ee211A_1_homework4

20105ee211A_1_homework4 - C D 1 E F G H 2 I 3 k(b In...

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1 EE 211A Digital Image Processing I Fall Quarter, 2010 Handout 11 Instructor: John Villasenor Homework 4 Due: Thursday, 21 October 2010 Reading: Textbook pp. 20-31, 132-180. 1. For the 2 x 2 transform A and the image U 3 1 2 3 1 , 1 2 2 1 3 A U = = - calculate the transformed image V and the basis images. 2. (a) Consider a 2D real sequence ) , ( n m u of size 4 × 4 whose DFT ) , ( l k v has been determined. Suppose that these data were stored on computer, and that a careless colleague has accidentally erased ), , ( n m u as well as several of the elements of ). , ( l k v Nine of the 16 elements of ) , ( l k v were not erased and are indicated below by the letters A through I. These letters may in general represent complex numbers. Where possible, give the missing elements of ) , ( l k v in terms of the letters A through I. Where this is not possible, write a question mark. 0 1 2 3 l 0 A
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Unformatted text preview: C D 1 E F G H 2 I 3 k (b) In general, the transform ) , ( l k v of a real 2D sequence is complex. However, there are some elements of ) , ( l k v ( , = = l k for example) which will always be real. Assuming that ) , ( n m u is real and of size , N N × where N is even, give the values of k , l for which ) , ( l k v will always be real. 2 3. Find the 2D unitary DFT ) , ( l k v of the following matrices: a) = 1 1 ) , ( n m u b) ( , ) 4 1 1 1 1 u m n = c) 1 1 1 1 1 ( , ) 1 1 4 1 1 j j j j u m n j j j j-- -- = -- -- 4. Find the 2D unitary DCT ) , ( l k v of the matrices in problem 2 parts (a) and (b)....
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