$H(s)=\frac{990}{(s+1)(s+100)}$

Using the impulse invariance method:

a$)$ Find the filter digital transfer function: $H[z].$ Assume the sampling rate Fs$=1000.(10$ points$)$

b$)$ For the above $H(s),$ determine the required minimum sampling rate, $Fs,$ and bandlimit frequency, $B,$ so that the maximum sampling error Set up the equation and approximate your solution when solving for B$.(10$ points$)$