ECE Ph.D. Qualifying Exam

Communication Signal (CS)

Question 5: Image Processing

August 2017 Problem 1


Solution

a)
$ ay(m,n)=ax(m,n)+a\lambda(x(m,n)-\dfrac{1}{9}\sum_{k=-1}^{1} \sum_{l=-1}^{1} x(m-k,n-l)) $ linear

b)
$ y(m,n)=x(m,n)+\lambda(x(m,n)-\dfrac{1}{9}\sum_{k=-1}^{1} \sum_{l=-1}^{1} x(m-k,n-l))=1.5x(m,n)-\dfrac{1}{18}\sum_{k=-1}^{1} \sum_{l=-1}^{1} x(m-k,n-l) $
$ h(m,n)=1.5\delta(m,n)-\dfrac{1}{18}(\delta(m+1)+\delta(m)+\delta(m-1))(\delta(n-1)+\delta(n)+\delta(n+1))) $
Wan82_CS5-1.PNG

c)
Not a separable system.

d)
$ H(e^{j\mu},e^{jv})=\dfrac{3}{2}-\dfrac{1}{18}\sum_{m=-1}^{1} e^{-j\mu}\sum_{n=-1}^{1} e^{-jv} =\dfrac{3}{2}-\dfrac{1}{18}(1+2cos\mu)(1+2cosv) $

e)
This is a sharpen filter. The image will become more sharpen as $ \lambda $ increases.


Similar Problem

2014 QE CS5 Prob2
2012 QE CS5 Prob2
2011 QE CS5 Prob1



Back to QE CS question 5, August 2017

Back to ECE Qualifying Exams (QE) page

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett