20105ee211A_1_homework5

20105ee211A_1_homework5 - 1 EE 211A Digital Image...

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Unformatted text preview: 1 EE 211A Digital Image Processing I Fall Quarter, 2010 Handout 15 Instructor: John Villasenor Homework 5 Due: Thursday, 4 November 2010 Reading: Textbook pp. 146 180. 1. Consider a random vector u consisting of two vectors below that occur with equal probability. - = 1 2 u and - = 2 1 u (a) Determine the autocorrelation matrix u R (not the covariance matrix) of . u (b) Find the orthonormal eigenvectors and associated eigenvalues of . u R (c) Give the matrix , * t which is used to obtain the forward KL transform of . u (d) Obtain the KL transforms n t n u v * = for . 1 , = n Verify that v represents an expansion of u in terms of the KL transform basis functions, i.e. that , ) 1 ( ) ( 1 v v u + = where n are columns of , or equivalently, conjugate of the rows of . * t (e) Find , v R the autocorrelation matrix of the vectors , n v and confirm that ), ( k v Diag R = where k are the eigenvalues of ....
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This note was uploaded on 04/18/2011 for the course EE 211A taught by Professor Villasenor during the Fall '10 term at UCLA.

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20105ee211A_1_homework5 - 1 EE 211A Digital Image...

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