## eSpeX Group Title 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

1. eSpeX Group Title

Is the 'del' symbolic of using the delta function?

2. mahmit2012 Group Title

Absolutely yes.

3. eSpeX Group Title

Could you please explain the logic you approach this with and how you handled the intervals where the function equaled a constant?

4. eSpeX Group Title

In my textbook, the delta function is not introduced for 4 more sections.

5. mahmit2012 Group Title

Do you know extended derivative with delta function?

6. mahmit2012 Group Title

Mathematician said there is no derivative in uncontinious point but engineers said it has.

7. mahmit2012 Group Title

@ali110 is one of them.

8. eSpeX Group Title

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)}

9. eSpeX Group Title

Those should be f(t)...

10. mahmit2012 Group Title

no, there is no information in an alone point for Laplace, but I made derivative to make an information then used the Laplace.

11. eSpeX Group Title

How did you make a derivative of a function that has only a constant value?

12. ali110 Group Title

L(f(t))=L(1)=1/s if for f(t)=t then L(f(t))=1/s^2

13. mahmit2012 Group Title

@ali110 is one of them.

14. ali110 Group Title

mohan gholami in which of them?

15. eSpeX Group Title

If it never equals 't', then do I only have $\frac{1}{s} +\frac{1}{s} +\frac{1}{s}$ ?

16. eSpeX Group Title

I believe he was saying that you were an engineer.

17. mahmit2012 Group Title

No, you have two points not two functions!

18. ali110 Group Title

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

19. mahmit2012 Group Title

Unfortunately Laplace transform doesn't sense points unless with delta function.

20. eSpeX Group Title

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?

21. ali110 Group Title

L(f(t))=L(3)=3L(1)=3*1/s=3/s

22. eSpeX Group Title

According to the book, the answer is 1/s. Does this mean that the laplace of t=1 and t=2 equate to 0?

23. ali110 Group Title

can we take laplace inverse at the end?

24. mahmit2012 Group Title

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.

25. eSpeX Group Title

So you would have: L{f(t)} = L{1} + L{3} + L{4} -> 1/s + 0 + 0 ?

26. mahmit2012 Group Title

ok I solve it with integral. int(0 inf) f(t)=1/s

27. mahmit2012 Group Title

You know the integral change the limit points to continues function and never sense them.

28. mahmit2012 Group Title

1 f'(t)=3del(t-1)-3del(t-1)+4del(t-2)-4del(t-2) and f(0)=1 L(f'(t))=3e^-s-3e^-s+4e^-2s-4e^-2s=sL(f(t))-1 L(f(t))=1/s(0+0+1)=1/s

29. mahmit2012 Group Title

I thought in two points 1 and 2 it has jumped so they were two alone points.

30. mahmit2012 Group Title

And Laplace has problem with the single points.

31. eSpeX Group Title

Ah. Okay, I will see if I can't apply this to the rest of my problems. Thank you very much.

32. mahmit2012 Group Title

You're welcome.

33. mahmit2012 Group Title

if the points in 1 and 2 was jumped so the solution was : 1 f'(t)=3del(t-1)+4del(t-2) 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)

34. eSpeX Group Title

But at this point I would have needed to use the integral approach since we have not reached the delta function?

35. ali110 Group Title

36. eSpeX Group Title

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.

37. mahmit2012 Group Title

But @ali110 there is no unit step and delta function! I guess Openhiem is the best refrence. Isn't it?

38. ali110 Group Title

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

39. ali110 Group Title

@mahmit2012

40. ali110 Group Title

L{f(t)} = L{1} + L{3} + L{4} -> 1/s + 0 + 0=1/s

41. ali110 Group Title

@eSpeX I GUESS

42. ali110 Group Title

@eSpeX CHECK laplace transform linearity property (in which one to one property)

43. eSpeX Group Title

Okay.

44. mahmit2012 Group Title

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.

45. eSpeX Group Title

Alright, I'll have to look up limit points then because I have not seen them yet as I recall.

46. KenLJW Group Title

You have to use the unit step function for 2 and 3 3u(t-1) 4u(t-2) for the first one I'd break it up u(t-1) - u(t-1minus) + u(t-1 plus) -u(t-2 minus) ect With these there's direct transformations

47. KenLJW Group Title

In EE the slope of the step function is an indication of bandwidth, if there was infinite bandwidth it would be a unit step