UnkleRhaukus
  • UnkleRhaukus
laplace transform of a periodic function/
Mathematics
schrodinger
  • schrodinger
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UnkleRhaukus
  • UnkleRhaukus
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UnkleRhaukus
  • UnkleRhaukus
im not very pleased with the final form of my answer,
UnkleRhaukus
  • UnkleRhaukus
mabye this is better \[F(p)=\frac{2}{(1-e^{-4p})p^2}-\frac{2e^{-2p}}{(1-e^{-4p})p^2}-\frac{4e^{-2p}}{(1-e^{-4p})p}\]

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anonymous
  • anonymous
yes this one is better but the one that you have solved is much better and simplified , so i dont think you need to do this
UnkleRhaukus
  • UnkleRhaukus
@lonliness , what region should i integrate for figure 2
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UnkleRhaukus
  • UnkleRhaukus
also how did go in this one
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anonymous
  • anonymous
|dw:1354803234598:dw|
anonymous
  • anonymous
|dw:1354803478460:dw|
anonymous
  • anonymous
|dw:1354803608097:dw|
UnkleRhaukus
  • UnkleRhaukus
but if i go from 0 to 2 pi ( in fig2) the the integral will be messy
anonymous
  • anonymous
wait !
UnkleRhaukus
  • UnkleRhaukus
ok
anonymous
  • anonymous
|dw:1354804514349:dw|
anonymous
  • anonymous
|dw:1354804529087:dw|
anonymous
  • anonymous
|dw:1354804592320:dw|
anonymous
  • anonymous
yes! your answer isn't correct because you had some mistake to solving integrals.
UnkleRhaukus
  • UnkleRhaukus
i see that now,
anonymous
  • anonymous
Do you know how I understood my mistake? Because I knew that the bounded signals should have Laplace with bounded limit in s=p=0
anonymous
  • anonymous
|dw:1354805030916:dw|
UnkleRhaukus
  • UnkleRhaukus
|dw:1354861124769:dw|
anonymous
  • anonymous
|dw:1354861368611:dw|
UnkleRhaukus
  • UnkleRhaukus
the slope is 1 and then -1
UnkleRhaukus
  • UnkleRhaukus
yes?
UnkleRhaukus
  • UnkleRhaukus
|dw:1354862069169:dw|
UnkleRhaukus
  • UnkleRhaukus
@mahmit2012
UnkleRhaukus
  • UnkleRhaukus
@TuringTest
anonymous
  • anonymous
@mahmit2012 s=ROC(region of convergence)+jw(frequency responce) so where the ROC of this function?
UnkleRhaukus
  • UnkleRhaukus
im not sure , i havent herd that term before, is it a restriction on p?
anonymous
  • anonymous
actually we moved from fourier transform to laplace transform because fourier transform tells only frequency responce of a signal/function but laplace transform can explain stability/unstability of function including with its frequency responce so its easy to design system by using laplace transform
anonymous
  • anonymous
|dw:1354866466108:dw|
anonymous
  • anonymous
\[F(s)=\int\limits_{-\infty}^{\infty}f(t)e^-st*dt\]
UnkleRhaukus
  • UnkleRhaukus
\[\delta=\sigma\]?
anonymous
  • anonymous
@UnkleRhaukus am i explain it more if u want?
UnkleRhaukus
  • UnkleRhaukus
yes please
anonymous
  • anonymous
oh yes \[s=\sigma+jw\] actually i have not seen it on table before
UnkleRhaukus
  • UnkleRhaukus
for some reason my text book has been using \(p\) for \(s\) \(x\) for \(t\) \(n\) fr \(\omega\) \(i\) for \(j\)
anonymous
  • anonymous
so for moving function(signal) |dw:1354867100786:dw| now for left sided signal |dw:1354867294896:dw| |dw:1354867371794:dw|
anonymous
  • anonymous
i am using book of ALAN.V.OPPENHEIM and also book of SAMARJIT.GHOSH
anonymous
  • anonymous
Have u know before why we use laplace transform?
UnkleRhaukus
  • UnkleRhaukus
do we use laplace transform to understand the frequencies of the system?
UnkleRhaukus
  • UnkleRhaukus
(also to solve Initial value problems )
anonymous
  • anonymous
yes we use laplace transform to find both frequency responce(jw) as well as its stabality and unstabaliy(sigma) of function s=sigma+jw as see above yes also for initial value problem+modulation problem+final value problem i can give u simple function matlab code if u want!!
UnkleRhaukus
  • UnkleRhaukus
yes i would be interested to try out your matlab code , also what is a modulation problem ?
anonymous
  • anonymous
modulation theorem!!!! application of signal and system in communication it is a technique that is use to convey the info over a long distance i.e for voice signal as voice signal dont have high range for long distance actual signal+carrier signal 3400hz+high freq signal(1 Mhz) voice data may die over a long distance if we not use carrier signal signal send for long distance through amplitude modulation as well as frequency modulation we can fix the band width of AM,short band width require if we want to send signal over a lond distance for FM,long band width is needed if we want to send signal for long distance but here there is some cost problem!!i will discuss if u want
anonymous
  • anonymous
but frequency modulation is best as noise signals in atmosphere donot affect on it like mobile phone signals we use frequency modulation technique!!! but still its so costly to use Freq modulation
UnkleRhaukus
  • UnkleRhaukus
ok, can you tell me more about the region of convergence for my triangles signal
anonymous
  • anonymous
i ask it for mohan gholami(@mahmit2012)!! he will tell u!!i think he know it!!!
anonymous
  • anonymous
btw fren which book u use for signals and systems can u tell me its authur name?
UnkleRhaukus
  • UnkleRhaukus
\[ \begin{align*} \mathcal L\big\{f(x)\big\}&=\int\limits_0^\infty f(x)e^{-px}\cdot\text dx\\ &=\tfrac1{1-e^{-4p}}\int\limits_0^{4}f(x)e^{-px}\cdot\text dx\\ &=\tfrac1{1-e^{-4p}}\left[\int\limits_0^{2}xe^{-px}\cdot\text dx+\int\limits_2^4(4-x)e^{-px}\cdot\text dx\right]\\ &=\tfrac1{1-e^{-4p}}\left[\frac{xe^{-px}}{-p}\Big|_0^2-\int\limits_0^{2}\frac{e^{-px}}{-p}\cdot\text dx+4\int\limits_2^4e^{-px}\cdot\text dx-\int\limits_2^4xe^{-px}\cdot\text dx\right]\\ &=\tfrac1{1-e^{-4p}}\left[\frac{2e^{-2p}}{-p}-\frac{e^{-px}}{p^2}\Big|_0^2+\frac{4e^{-px}}{-p}\Big|_2^4-\frac{xe^{-px}}{-p}\Big|_2^4+\int\limits_2^{4}\frac{e^{-px}}{-p}\cdot\text dx\right]\\ &=\tfrac1{1-e^{-4p}}\left[\frac{-2e^{-2p}}{p}-\frac{e^{-2p}-1}{p^2}+\frac{4e^{-4p}-4e^{-2p}}{-p}-\tfrac{4e^{-4p}-2e^{-2p}}{-p}+\frac{e^{-px}}{p^2}\Big|_2^4\right]\\ &=\tfrac1{1-e^{-4p}}\left[\frac{-2e^{-2p}}{p}+\frac{1-e^{-2p}}{p^2}+\frac{2e^{-2p}}{p}+\frac{e^{-4p}-e^{-2p}}{p^2}\right]\\ &=\frac1{1-e^{-4p}}\left[\frac{1-2e^{-2p}+4e^{-4p}}{p^2}\right]\\ &=\frac{1-2e^{-2p}+4e^{-4p}}{(1-e^{-4p})p^2}\\ \end{align*}\]
UnkleRhaukus
  • UnkleRhaukus
is this right for the wave of triangles?
UnkleRhaukus
  • UnkleRhaukus
is there some way to check?
UnkleRhaukus
  • UnkleRhaukus
@sirm3d
UnkleRhaukus
  • UnkleRhaukus
http://www.wolframalpha.com/input/?i=inverse+laplace+transform+of+%281-2e%5E%28-2s%29%2B4e%5E%28-4s%29%29%2F%28%281-e%5E%28-4s%29%29s%5E2%29 .. damn it
UnkleRhaukus
  • UnkleRhaukus
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