{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20105ee211A_1_homework5

# 20105ee211A_1_homework5 - EE 211A Fall Quarter 2010...

This preview shows pages 1–2. Sign up to view the full content.

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 0 u and - = 0 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 φ which is used to obtain the forward KL transform of . u (d) Obtain the KL transforms n t n u v * φ = for . 1 , 0 = n Verify that 0 v represents an expansion of 0 u in terms of the KL transform basis functions, i.e. that , ) 1 ( ) 0 ( 1 0 0 0 0 φ φ v v u + = where n φ are columns of , φ or equivalently, conjugate of the rows of . * t φ (e) Find , v R the autocorrelation matrix of the vectors , n v and confirm that ), ( k v Diag R λ = where k λ are the eigenvalues of .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

20105ee211A_1_homework5 - EE 211A Fall Quarter 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online