7 The Bilinear Transform (10 pts) In class, we were told that the bilinear transform maps the left half-plane (LHP) inside of the unit circle. Thus, stable poles in the

s-plane will be located within the unit circle in the-plane. Prove that poles that are in the LHP will be mapped inside the unit circle. Hints: \bullet s=\sigma+j \omega • The bilinear transform for H(2) is obtained by substituting H(s) with H(z)=H_{c}\left(\frac{2}{T_{d}} \cdot \frac{1-z^{-1}}{1+z^{-1}}\right) You must show your work. Simply stating that the poles of H(z) are within the unit circle when the poles of H.(s) are in the LHP will result in no credit.