(a) The following transfer function is a lag network designed to introduce a gain attenuation of \(10(-20 \mathrm{~dB})\) at \(\omega=3 \mathrm{rad} / \mathrm{sec}\),

\[H(s)=\frac{10 s+1}{100 s+1}\]

Assume a sampling period of \(T=0.25 \mathrm{sec}\), and compute and plot in the \(z\)-plane the pole and zero locations of the digital implementations of \(H(s)\) obtained using (1) Tustin's method and (2) polezero mapping. For each case, compute the amount of gain attenuation provided by the network at \(z_{1}=e^{j \omega T}\).

(b) For each of the equivalent digital systems in part (a), plot the Bode magnitude curves over the frequency range \(\omega=0.01\) to \(10 \mathrm{rad} / \mathrm{sec}\).