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))) $
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.
