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Fourier transtorm [40 pts] Write the following function g(t) in terms of Heaviside step function:for <1 2t _ 2 for 1 < I < 2 21 _ 1 for 2 < / < 3 for...

Question

Fourier transtorm [40 pts] Write the following function g(t) in terms of Heaviside step function:for <1 2t _ 2 for 1 < I < 2 21 _ 1 for 2 < / < 3 for 3 < |Find the derivative of g(t) (show all steps)

Fourier transtorm [40 pts] Write the following function g(t) in terms of Heaviside step function: for <1 2t _ 2 for 1 < I < 2 21 _ 1 for 2 < / < 3 for 3 < | Find the derivative of g(t) (show all steps)



Answers

Find the Laplace transform of the given function. In Problem 27 assume that term-by-term integration of the infinite series is permissible. $$ f(t)=\left\{\begin{array}{ll}{1,} & {0 \leq t<1} \\ {0,} & {1 \leq t<2} \\ {1,} & {2 \leq t<3} \\ {0,} & {t \geq 3}\end{array}\right. $$

Hello and Welcome to Probleble 25 of Chapter six. Section 3 we were asked to find a little place transform of the given function and it's a piecewise function which means we can write this in terms of heavy sides so you can do that now. Um from 0 to 1 we're gonna start at one. So we know the base is one From 1-2 you go back to zero which means what we're doing is subtracting one and that can be done by subtracting the heavy side function of one. Then we go up to one again By the same argument we will have you add use of two T. And then again when he hits three We're gonna go back to zero. So we'll subtract U sub three of 2. And that's what FFT is Now from uh chapter 6.3 we learned the applause transform of heavy side function which is E to the minus C. S over S or C. Is the subscript character there. So uh with that we can just take the lobos transform of this entire thing. So capital F. Of S. Which is the well plus transform of the F. F. T. Yeah is equal to one minus E. To the minus us plus E. To the minus two S -E. to the -3 s. All over us. And that concludes our problem


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