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Laplace Transform: Evaluate L{f(t)}
\[\begin {align*} f(t) &= 1 ,\ t \ge 0, \quad t \neq 1, \ t \neq 2 \\
&= 3,\ t = 1\\
&= 4,\ t = 2\end {align*} \]
Would appreciate someone explaining how to set this up and evaluate.
 one year ago
 one year ago
Laplace Transform: Evaluate L{f(t)} \[\begin {align*} f(t) &= 1 ,\ t \ge 0, \quad t \neq 1, \ t \neq 2 \\ &= 3,\ t = 1\\ &= 4,\ t = 2\end {align*} \] Would appreciate someone explaining how to set this up and evaluate.
 one year ago
 one year ago

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eSpeXBest ResponseYou've already chosen the best response.0
Is the 'del' symbolic of using the delta function?
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
Could you please explain the logic you approach this with and how you handled the intervals where the function equaled a constant?
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
In my textbook, the delta function is not introduced for 4 more sections.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
Do you know extended derivative with delta function?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
Mathematician said there is no derivative in uncontinious point but engineers said it has.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
@ali110 is one of them.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
So far what I know of piecewise functions is that L{f(x)} = L{f_1(x)} + L{f_2(x)} + L{f_3(x)}
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
no, there is no information in an alone point for Laplace, but I made derivative to make an information then used the Laplace.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
How did you make a derivative of a function that has only a constant value?
 one year ago

ali110Best ResponseYou've already chosen the best response.0
L(f(t))=L(1)=1/s if for f(t)=t then L(f(t))=1/s^2
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
@ali110 is one of them.
 one year ago

ali110Best ResponseYou've already chosen the best response.0
mohan gholami in which of them?
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
If it never equals 't', then do I only have \[\frac{1}{s} +\frac{1}{s} +\frac{1}{s}\] ?
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
I believe he was saying that you were an engineer.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
No, you have two points not two functions!
 one year ago

ali110Best ResponseYou've already chosen the best response.0
oh i am an electrical engineering student of 5th semester who got 71 marks out of 100 in laplace transform in his 4th semster:))) @eSpeX
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
Unfortunately Laplace transform doesn't sense points unless with delta function.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
Laplace does not make sense to me on how to handle them, and with respect to this piecewise I do not see how it will be done if we have not been shown the delta function. Is it something (or similar) to the heavyside step function?
 one year ago

ali110Best ResponseYou've already chosen the best response.0
L(f(t))=L(3)=3L(1)=3*1/s=3/s
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
According to the book, the answer is 1/s. Does this mean that the laplace of t=1 and t=2 equate to 0?
 one year ago

ali110Best ResponseYou've already chosen the best response.0
can we take laplace inverse at the end?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
No the answer is just 1/s because Laplace transform can not sense limit points, and it just follow the infinity points which defined with delta function.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
So you would have: L{f(t)} = L{1} + L{3} + L{4} > 1/s + 0 + 0 ?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
ok I solve it with integral. int(0 inf) f(t)=1/s
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
You know the integral change the limit points to continues function and never sense them.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
1 f'(t)=3del(t1)3del(t1)+4del(t2)4del(t2) and f(0)=1 L(f'(t))=3e^s3e^s+4e^2s4e^2s=sL(f(t))1 L(f(t))=1/s(0+0+1)=1/s
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
I thought in two points 1 and 2 it has jumped so they were two alone points.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
And Laplace has problem with the single points.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
Ah. Okay, I will see if I can't apply this to the rest of my problems. Thank you very much.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
if the points in 1 and 2 was jumped so the solution was : 1 f'(t)=3del(t1)+4del(t2) and f(0)=1 L(f'(t))=3e^s+4e^2s=sL(f(t))1 L(f(t))=1/s(3e^s+4e^2s+1)
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
But at this point I would have needed to use the integral approach since we have not reached the delta function?
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
It appears that all of those examples have a range that the integral is evaluated over. So none of the laplace methods evaluate a point.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
But @ali110 there is no unit step and delta function! I guess Openhiem is the best refrence. Isn't it?
 one year ago

ali110Best ResponseYou've already chosen the best response.0
check page 11 and every problem will solve as writer show that for t not equal to 1 And 2 as in above question F=0 and Agha! i love alan V openheim as i take all his video lectures about signals and systems but in our engineerig college we study Indian professor Ghosh sumarjit check his book on Signal and system and about fourier series more intersesting then oppenheim
 one year ago

ali110Best ResponseYou've already chosen the best response.0
L{f(t)} = L{1} + L{3} + L{4} > 1/s + 0 + 0=1/s
 one year ago

ali110Best ResponseYou've already chosen the best response.0
@eSpeX CHECK laplace transform linearity property (in which one to one property)
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
Ok. And I should mention that don't use L(3)=0 because it is not true. You can write L*(3)=0 and define L* means Laplace for limit points.
 one year ago

eSpeXBest ResponseYou've already chosen the best response.0
Alright, I'll have to look up limit points then because I have not seen them yet as I recall.
 one year ago

KenLJWBest ResponseYou've already chosen the best response.0
You have to use the unit step function for 2 and 3 3u(t1) 4u(t2) for the first one I'd break it up u(t1)  u(t1minus) + u(t1 plus) u(t2 minus) ect With these there's direct transformations
 11 months ago

KenLJWBest ResponseYou've already chosen the best response.0
In EE the slope of the step function is an indication of bandwidth, if there was infinite bandwidth it would be a unit step
 11 months ago
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