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Plot the graph of the square wave function defined as $$f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t)$$ on the interval $t>0$ and find its Laplace transform. The http://mathworld.wolfram.com/FourierSeriesSquareWave.html has FourierSeriesSquareWave but not exactly as the function above. Please, can anyone help out in plotting this graph and solving the problem? Thanks for your time and help!

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  • $\begingroup$ I don't get you question. What is $h_n$? $\endgroup$
    – Henrik Schumacher
    Aug 19, 2018 at 19:37
  • $\begingroup$ @Henrik Schumacher: $h_n$ is heaviside function! $\endgroup$
    – Omojola Micheal
    Aug 19, 2018 at 19:40
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    $\begingroup$ Oha. There is more then one Heaviside function? Really, poorly stated questions have a low chance to be answered properly. Please provide all relevant information. $\endgroup$
    – Henrik Schumacher
    Aug 19, 2018 at 19:42
  • $\begingroup$ @Henrik Schumacher: Okay, I'll do that! $\endgroup$
    – Omojola Micheal
    Aug 19, 2018 at 19:43
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    $\begingroup$ Is this f = Sum[(-1)^n*HeavisideTheta[t - n], {n, 0, 10}] g = LaplaceTransform[f, t, s] Plot[f, {t, 0, 10}] Plot[g, { s, 0, 10}] close to what you are looking for? Note: make sure each of those four expressions is on a separate line or in a separate cell in your notebook $\endgroup$
    – Bill
    Aug 19, 2018 at 20:01

1 Answer 1

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Why not use SquareWave instead?

f[t_] := SquareWave[t/2]

Visualization:

Plot[f[t], {t, 0, 10}]

enter image description here

The LaplaceTransform:

LaplaceTransform[f[t], t, s]

Tanh[s/2]/s

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