Solution:

For $N=3$, the transfer function of a normalized Butterworth filter is given by,

$ \begin{aligned}\\ H(s) & =\frac{1}{(s+1)\left(s^2+s+1\right)} \\\\ & =\frac{A}{s+1}+\frac{B}{s+0.5+j 0.866}+\frac{C}{s+0.5-j 0.866}\\ \end{aligned}\\ $

$ \begin{aligned} A & =\left.(s+1) \frac{1}{(s+1)\left(s^2+s+1\right)}\right|_{s=-1}=\frac{1}{(-1)^2-1+1}=1 \\\\ B & =\left.(s+0.5+j 0.866) \frac{1}{(s+1)(s+0.5+j 0.866)}\right|_{s=-0.5-j 0.866} \\\\ & =\frac{1}{(-0.5-j 0.866+1)(-j 0.866-j 0.866)} \\\\ & =\frac{1}{-j 1.732(0.5-j …