Question #111960

find continued fraction expansion of the following impedance function.

z(s)=(s^5 + 4 s^3 + 5 s)/(3 s^4 + 6 s^2)

z(s)=(s^5 + 4 s^3 + 5 s)/(3 s^4 + 6 s^2)

Expert's answer

First, let us divide by as usual numbers. We need to multiply by , to cancel . Subtracting , obtain remainder , so no further reduction is possible.

Hence, , from where .

The remainder has degree of polynomial in the numerator smaller, than degree of the denominator. Hence, we can decompose it into partial fractions: , from where equating the coefficients next to powers of in the left and right hand sides of previous equation, obtain linear system, from where .

Therefore, , and finally

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