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anonymous
 one year ago
How to get the laplace inverse for a fraction a complex poles at Sdomain ?
anonymous
 one year ago
How to get the laplace inverse for a fraction a complex poles at Sdomain ?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a fraction a complex poles at sdomain? can you clarify what you mean?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you have a rational expression \(F(s)=P(s)/Q(s)\) where \(P(s)=k(sz_1)\cdots(sz_m),Q(s)=(sp_1)\cdots(sp_n)\) where \(z_i,p_j\) are the zeros and poles of \(F\) then we can use Mellin's inversion formula as normal: $$f(t)=\int_{\gamma} e^{st}F(s)\ ds$$where \(\gamma\) is given by the line \((s_0i\infty, s_0+i\infty)\) where \(s_0\) is chosen to ensure \(F\) is wellbehaved along this line; in particular, it is sufficient to pick \(s_0>\maxp_j\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is basically just the inverse Fourier transform taking into account that we need exponentials to tame asymptotic behavior
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