Academic Guidance ""Laplace""This questions are important for my master degree.. thanks for helpings

romsek

Math Team
Sep 2015
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You give us questions in a language the bulk of us don't speak and you post it as an image so we can't even cut and paste it into google translate.

You must not want help very badly.
 

skipjack

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Dec 2006
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It's Turkish. Prove the formula for #1 and obtain the Z-transform or Laplace transform for the rest, noting that "ters" means "inverse".

4.$\ $ (2s + 14)/(s² + 4s + 8) = 2(s + 2)/((s + 2)² + 4) + 10/((s + 2)² + 4),
$\ \ \ \ $so its inverse Laplace transform is e$^{-2\text{t}}$(2cos(2t) + 5sin(2t)).
 
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romsek

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You can do (3) by inspection.

By definition $X(z) = \sum \limits_{n=-\infty}^\infty~X(n) z^{-n}$

Thus we see
$X(n)=\begin{cases}n &n=5,6,7,8\\0&\text{else}\end{cases}$
 
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romsek

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#2

$Z\left\{f(n-k)\right\} = z^{-k}Z\{f(n)\}$

$Z\{\delta(n)\} = \sum \limits_{n=-\infty}^\infty~\delta(n)z^{-n} = z^{-0} = 1$

$Z\{\sum \limits_{k=1}^4~(k+1) \delta(n-k)\} = \sum \limits_{k=1}^4 (k+1) z^{-k}$
 
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skipjack

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Dec 2006
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Check your working for question 4.