Obtain digital filter transfer function by applying impulse invariance transfer function,,

$$ H(s)=\frac{s}{(s+5)(s+2)} \quad \text { if } \mathrm{Ts}=0.1 s $$

Solution:

$$ \text { Given } H(s)=\frac{s}{(s+5)(s+2)} $$

step 1- Obtain $h(t)$ by I.L.T By PFE,

$ \begin{aligned}\\ & H(s)=\frac{A}{S+5}+\frac{B}{S+2} \\\\ & A=\left.(s+5) H(s)\right|_{s=-5} \quad B=\left.(s+2) H(s)\right|_{s=-2}\\ \end{aligned}\\ $

$ \begin{aligned}\\ & A=5 / 3 \quad B=-2 / 3 \\\\ & H(s)=\frac{5 / 3}{5+5}-\frac{2 / 3}{5+2} \\\\ & n(t)=\frac{5}{3} e^{-5 …