Consider the transfer function
$$H_{c}(S) = \frac{1}{(s+1)(s+3)}$$
Bilinear transformation with a sampling period of $0.1 \; \text{s}$ is employed to obtain the discrete-time transfer function $H_{d}(z).$ Then $H_{d}(z)$ is __________
- $\frac{(1+z^{-1})^{2}} {(19-21z^{-1}) (23-17z^{-1})}$
- $\frac{(1-z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$
- $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (23-17z^{-1})}$
- $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$