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Find analytic description of low pass filtered signal

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twig27

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Hello,
suppose there is a bessel filter (2nd order low pass) which has the following transfer function:
\[ TF_{Bessel}(s) = \frac{a_1}{a_1+b_1s+s^2} \].
I apply an input voltage of the form:
\[V_{in}(s) = \frac{V}{s} \]
I would like to find an anlytic description of the bessel output.

Calculating the inverse laplace transform of the multiplication of the two, does not really work when I use matlab. I guess it has problems with the complex poles of the bessel filter. Thanks for any hints!\[\nu\]
 

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