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b)<br> | b)<br> | ||
<math>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}))</math><br> | <math>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}))</math><br> | ||
| + | <br> | ||
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| + | c)<br> | ||
| + | minimum sampling frequency <math>\dfrac{1}{T}>=\dfrac{2}{a}</math> <math>f>=\dfrac{2}{a}</math> <math>T<=\dfrac{a}{2}</math><br> | ||
| + | <br> | ||
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| + | d)<br> | ||
| + | <math>T=\dfrac{a}{2}</math><br> | ||
| + | https://www.projectrhea.org/rhea/dropbox_/381ea5db244c12bb92e6de3206725a7a/Wan82_CS5-3.PNG<br> | ||
| + | <br> | ||
| + | |||
| + | e)<br> | ||
| + | <math>T=a</math><br> | ||
| + | https://www.projectrhea.org/rhea/dropbox_/381ea5db244c12bb92e6de3206725a7a/Wan82_CS5-4.PNG<br> | ||
<br> | <br> | ||
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Revision as of 14:24, 19 February 2019
Communication Signal (CS)
Question 5: Image Processing
August 2017 Problem 2
Solution
a)
$ sinc^2(\dfrac{t}{a}) \Rightarrow |a|\Lambda(af) $ (CTFT)
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}>=\dfrac{2}{a} $ $ f>=\dfrac{2}{a} $ $ T<=\dfrac{a}{2} $
d)
$ T=\dfrac{a}{2} $
e)
$ T=a $
