Could I please have the worked solution for the question as follows:

(a) Show that if H(s) can be factorised as: H(s)=i=1Nspiki then H(z) can be written: H(z)=i=1N1epiTz1ki i.e. a digital filter design based on the impulse invariance method. In developing your derivation remember: The inverse Laplace transform of spi1 is: epttu(t) (where u(t) is the unit step function) The geometric series sum: 1+cz1+c2z2+c3z3 converges to: 1cz11 (for all cz1