ECE Ph.D. Qualifying Exam

Communication Signal (CS)

Question 5: Image Processing

August 2017 Problem 2


Solution

a)
$ sinc^2(\dfrac{t}{a}) \Rightarrow |a|\Lambda(af) $ (CTFT)
Wan82_CS5-2.PNG

b)
$ y(n)=sinc^2(\dfrac{nT}{a}) \Rightarrow X_s(f)=\dfrac{1}{T}\sum_{k=-\infty}^{\infty} X(f-kF)=\dfrac{|a|}{T}\sum_{k=-\infty}^{\infty}\Lambda(a(f-\dfrac{k}{T})) $

c)
minimum sampling frequency $ \dfrac{1}{T}\ge\dfrac{2}{a} $ $ f\ge\dfrac{2}{a} $ $ T\le\dfrac{a}{2} $

d)
$ T=\dfrac{a}{2} $
Wan82_CS5-3.PNG

e)
$ T=a $
Wan82_CS5-4.PNG


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